How to Convert Percent to Decimal in 2 Easy Steps

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How to Convert Percent to Decimal in 2 Easy Steps

How to Convert Percent to Decimal in 2 Easy Steps

Math Skills: How Do You Convert a Percent to Decimal?

 

Free Step-by-Step Guide: How to Convert Percent to Decimal

 

Every math student must learn and understand how to convert percent to decimal. This simple math skill has tons of practical applications both inside the classroom and in real life as well.

In this free guide to How to Convert Percent to Decimal, you will learn an easy two-step method for converting any percent into a decimal. Once you learn how to apply the two-steps, you will be able to quickly and accurately turn percents to decimals. The guide covers the following subtopics, and you can use the quick-links below to jump to a section of interest if you wish:

Once you work through the examples in this guide, you will have a strong understanding of how to turn percent to decimal in a variety of cases.

Are you ready to get started?

 

Lesson Preview: How to Convert Percent to Decimal Explained

 

How to Convert Percent to Decimal

We will begin this guide to converting percents into decimals by reviewing a few important vocabulary terms in reference to percentages and decimals.

Definition: In math, a percentage (or a percent) is a value or number that can be expressed as a fraction with where the denominator is 100. For example, 25% is equivalent to the fraction 25/100.

Definition: In math, a decimal is a value that represents a whole number with a fractional part. The fractional part will always have a denominator that is equal to 10 or a multiple of 10. For example, the decimal 0.8 is equal to the fraction 8/10.

Percents and decimals have a proportional relationship and they both can be used to represent a value. Whether you choose to express values as percents or as decimals often depends on the situation. Sometimes, it makes more sense to represent values as percents, and other times it is more useful to express values in decimal form. Given this relationship between percents and decimals, it is incredibly useful for you to be able to quickly and accurately convert between the two, especially converting a percent to decimal.

 

Figure 01: How to Convert Percent to Decimal: 85% converted to a decimal is 0.85

 

How to Convert Percent to Decimal in 2 Steps

Now that we have reviewed the key vocabulary terms and relationships related to percents and decimals, we are ready to learn how to turn percent to decimal by following two simple steps:

  • Step One: Rewrite the percent without the % symbol

  • Step Two: Add a decimal point (if there isn’t one already) and shift it two places to the left

If you can learn how to apply these two simple step s, you will be able to successfully convert any percent into a decimal number.

For example, let’s apply these two steps to converting 85% into a decimal number.

Step One: Rewrite the percent without the % symbol

For the first step, we simply have to take the percentage value and rewrite it without the % symbol as follows:

  • 85% → 85

Now we can move onto Step Two.

Step Two: Add a decimal point (if there isn’t one already) and shift it two places to the left

For the second step, we have to see if the result from Step One has a decimal point. If it doesn’t already have one, we have to add one. Then, we just have to take that decimal point and shift it two units to the left as follows:

  • 85 → 85.0

  • 85.0 → .85 → 0.85

Final Answer: 85% = 0.85

That’s all that there is to it!

 

Figure 02: You can convert a percent to decimal by shifting the decimal place two places to the left.

 

Ready to gain some more experience with using our two-step method for how to turn percent to decimal? Let’s move onto the next section where we will work through five different examples.

How Do You Convert a Percent to Decimal?

Convert Percent to Decimal Example #1

Example: Convert 40% to a decimal.

For Example #1, we have to convert 40% to a decimal number. We can solve this problem by following our two-step method as follows:

Step One: Rewrite the percent without the % symbol

We can complete Step One by rewriting 40% without a percentage symbol as follows:

  • 40% → 40

Step Two: Add a decimal point (if there isn’t one already) and shift it two places to the left

Since our result from Step One, 40, doesn’t have a decimal point, we have to add one and then move it two places to the left as follows:

  • 40 → 40.0

  • 40.0 → .4 → 0.4

Final Answer: 40% = 0.4

We have now solved the first example and we can say that 40% is equal to 0.4.

Figure 03 below illustrates how we used our two-step method to solve this first problem.

 

Figure 03: How to Convert Percent to Decimal: 40% = 0.4

 

Are you ready to try another example?

Convert Percent to Decimal Example #2

Example: Convert 79% to a decimal.

For this next example, we can again use our two-step method for converting percents to decimals as follows:

Step One: Rewrite the percent without the % symbol

Just like the last example, we start off by rewriting the percent value without the % symbol as follows:

  • 79% → 79

Step Two: Add a decimal point (if there isn’t one already) and shift it two places to the left

Since 79 does not have a decimal point, we have to add one and then shift it to the left two places.

  • 79 → 79.0

  • 79.0 → .79 → 0.79

Final Answer: 79% = 0.79

So, we can conclude that 79% is equal to 0.79.

Figure 04 displays how we solved Example #2.

 

Figure 04: How do you convert a percent to decimal?

 

Convert Percent to Decimal Example #3

Example: Convert 3% to a decimal.

Are you starting to get the hang of it? Let’s move onto to this third example, where we have to convert 3% into a decimal value.

Step One: Rewrite the percent without the % symbol

Start off by rewriting 3% without the percentage symbol:

  • 3% → 3

Step Two: Add a decimal point (if there isn’t one already) and shift it two places to the left

 
3% = 0.03

3%=0.03

 

Next, we have to add a decimal point and then shift it two places to the left as follows:

  • 3 → 3.0

  • 3.0 → .03 → 0.03

Final Answer: 3% = 0.03

Finally, we can conclude that 3% is equal to 0.03.

The entire step-by-step process for converting this percent to decimal is shown in Figure 05 below.

 

Figure 05: How to Turn Percent to Decimal: 3% = 0.03

 

Convert Percent to Decimal Example #4

Example: Convert 6.2% to a decimal.

For this fourth example, we are dealing with a percentage that includes a decimal. Luckily, we can still use our two-step method to convert to percent to a decimal.

Step One: Rewrite the percent without the % symbol

Just like the previous examples, our first step is to rewrite the percent without the % sign.

  • 6.2% → 6.2

Step Two: Add a decimal point (if there isn’t one already) and shift it two places to the left

 

6% = 0.062

 

In this case, we don’t have to add a decimal because there already is one (between 6 and 2 in 6.2). So, we just have to take that decimal point and shift it two places to the left as follows:

  • 6.2 → .062 → 0.062

Final Answer: 6.2% = 0.062

The entire step-by-step process for converting this percent to decimal is shown in Figure 06 below.

 

Figure 06: How to Convert Percent to Decimal Example #4

 

Convert Percent to Decimal Example #5

Example: Convert 115% to a decimal.

For our fifth and final example, we have to convert a percent that is great than 100% into a decimal. Even in situations like, we can still use our two-step method to accurately convert the percent to decimal.

Step One: Rewrite the percent without the % symbol

Just like all of the previous examples, we start out by rewriting 115% without the percent symbol as follows:

  • 115% → 115

Step Two: Add a decimal point (if there isn’t one already) and shift it two places to the left

 

115% = 1.15

 

To complete Step Two, we just have to add a decimal point at the end 115 and then shift it two places to the left as follows:

  • 115 → 115.0

  • 115.0 → 1.150 → 1.15

Note that we don’t have to include the zero at the end of 1.150 and we can conclude that:

Final Answer: 115% = 1.15

All of the steps that were followed to complete this last example are shown in Figure 07 below.

 

Figure 07: How to convert percent to decimal when the percent is greater than 100.

 

Conclusion: How to Convert Percent to Decimal

Being able to quickly and accurately convert a percent to a decimal is an important and useful math skill that every student must master.

You can successfully convert any percent into a decimal by following two simple steps:

  • Step One: Rewrite the percent without the % symbol

  • Step Two: Add a decimal point (if there isn’t one already) and shift it two places to the left

In this guide on how to turn percent to decimal, we worked through five step-by-step examples where we made the following conversions:

  • 40% = 0.4

  • 79% = 0.79

  • 3% = 0.03

  • 6.2% = 0.062

  • 115% = 1.15

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How to Convert Decimal to Percent in 2 Easy Steps

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How to Convert Decimal to Percent in 2 Easy Steps

How to Convert Decimal to Percent in 2 Easy Steps

Math Skills: How Do You Convert a Decimal to Percent?

 

Learn how to convert decimal to percent.

 

Understanding how to convert decimal to percent is an important and useful math skill with applications inside the classroom and in the real world.

This free Step-by-Step Guide on How to Convert Decimal to Percent will teach you a simple 2-step method to converting a decimal to a percent whenever you are solving math problems are dealing with real-world scenarios involving decimals and percents. This free guide is organized based on the following topics:

You can work through each section in sequential order, or you can click on any of the text links above to jump to any particular section of this guide.

Are you ready to learn how to convert decimal to percent? Let’s get started!

 

Lesson Preview: How to Convert Decimal to Percent in Two Steps.

 

How to Convert a Decimal to a Percent

Before we learn the step-by-step process for how to convert a decimal to a percent, it’s important that you understand some key vocabulary and concepts related to decimals and percents.

Definition: In math, a decimal is a way of expressing a whole number that has a fractional part (where the fractional part is always out of 10 or a multiple of 10). These types of numbers include a whole number and a fractional part that are separated by a decimal point.

Definition: In math, a percent is a number that can be expressed as a fraction with a denominator of 100.

Whenever you are converting a decimal to a percent, you are essentially converting a fraction with a denominator of 10 (or a multiple of 10) to a fraction with a denominator of 100.

It is important to note that decimals and percents are two different ways to express the same value. In some cases, it will be more useful to work with numbers as decimals. And, in other cases, it will be more useful to work with numbers as percents. Knowing how to easily convert a decimal to percent will allow you to be successful in both types of situations.

 

Figure 01: The decimal 0.75 converted to a percent is 75%. Both values represent 75/100.

 

How to Convert a Decimal to a Percent in 2 Steps

Now that you are familiar with the relationship between a decimal and a percent, you are ready to learn our easy 2-step method for how to convert a decimal to percent.

  • Step One: Multiply the Decimal Value by 100

  • Step Two: Write the Result as a Percentage.

As long as you can follow these two steps, you can easily convert a decimal to a percent.

For example, let’s use our two-step method to convert the decimal 0.75 to a percent.

Step One: Multiply the Decimal Value by 100

Our first step is to take the decimal 0.75 and multiply it by 100 as follows:

  • 0.75 x 100 = 75

Note that multiplying a decimal by 100 is the same as taking the decimal point and moving it two places to the right. In this case, multiplying 0.75 results in 75.0, or just 75.

Step Two: Write the Result as a Percentage.

The next step is to take your result from Step One and express it as a percentage as follows:

  • 75 → 75%

Final Answer: 0.75 = 75%

Note that you can express your final answer as 75% or 75.0% (either one is correct).

 

Figure 02: You can convert a decimal to a percent by multiplying the decimal by 100 (or simply by shifting the decimal point two places to the right).

 

Now that you know how to convert a decimal to percent using our 2-step method, let’s gain some more practice and experience making conversions by working through a few more practice problems.

How Do You Convert a Decimal to Percent?

Convert Decimal to Percent Example #1

Example: Convert 0.5 to a percent.

For this first example, we want to convert the decimal 0.5 to a percent. We can make this conversion by following our 2-step method as follows:

Step One: Multiply the Decimal Value by 100

For Step One, we have to multiply the decimal value 0.5 by 100 as follows:

  • 0.5 x 100 = 50

Again, if you are unsure of how to multiply a decimal by 100, you can find the answer simply by shifting the decimal point two places to the right.

Step Two: Write the Result as a Percentage.

Finally, we have to take our result from Step One and express it as a percent (i.e. express the value from Step One with a percentage sign attached to it) as follows:

  • 50 → 50%

Final Answer: 0.50 = 50%

So, we can say that the decimal 0.50 is equal to 50%.

The step-by-step process for solving this first example is illustrated in Figure 03 below.

 

Figure 03: How to Convert Decimal to Percent.

 

Now, let’s move onto the next example.

Convert Decimal to Percent Example #2

Example: Convert 0.36 to a percent.

Let’s go ahead and use our two-step method to solve this next example.

Step One: Multiply the Decimal Value by 100

Just like we did in the last example, our first step to converting a decimal to percent is to multiply the percent by 100:

  • 0.36 x 100 = 36

Remember that multiplying a decimal by 100 is the same thing as moving the decimal point two places to the right.

Step Two: Write the Result as a Percentage.

For the second step, we have to express our result from Step One as a percentage:

  • 36 → 36%

Final Answer: 0.36 = 36%

Are you starting the get the hang of it? Figure 04 below shows how we used our two-step method to solve Example #2.

 

Figure 04: How Do You Convert a Decimal to Percent?

 

Convert Decimal to Percent Example #3

Example: Convert 0.08 to a percent.

For this third example, we can again use our 2-step method to make this conversion:

Step One: Multiply the Decimal Value by 100

First, multiply the decimal by 100:

  • 0.08 x 100 = 8

You could have also just moved the decimal point to places to the right as follows:

  • 0.08 → 8.0 or 8

Step Two: Write the Result as a Percentage.

Next, we just have to express our result from Step One as a percentage:

  • 8 → 8%

Final Answer: 0.08 = 8%

Figure 05 below illustrates how we solved Example #3.

 

Figure 05: Decimal to Percent: 0.08 = 8%

 

Convert Decimal to Percent Example #4

Example: Convert 0.045 to a percent.

Let’s continue using our two-step method to solve this problem:

Step One: Multiply the Decimal Value by 100

Start off by multiplying the decimal by 100:

  • 0.045 x 100 = 4.5

Note that you would end up with the same result (4.5) if you had just moved the decimal point two places to the right:

  • 0.045 → 4.5

Step Two: Write the Result as a Percentage.

Finally, we can express the result from Step One as a percent as follows:

  • 4.5 → 4.5%

Final Answer: 0.045 = 4.5%

 

Figure 06: Convert a Decimal to Percent: 0.045 = 4.5%

 

Convert Decimal to Percent Example #5

Example: Convert 1.39 to a percent.

We can use our two-step method for how to convert decimal to percent to solve this final example:

Step One: Multiply the Decimal Value by 100

The first step is to multiply the decimal by 100 as follows:

  • 1.39 x 100 = 139

Step Two: Write the Result as a Percentage.

Next, express the answer from the first step as follows:

  • 139 → 139%

Final Answer: 1.39 = 139%

 

Figure 07: Decimal to Percent Conversion: Example #5

 

Conclusion: How to Convert Decimal to Percent

Knowing how to quickly convert decimal to percent is a useful and important math skill with many academic and real-world applications.

You can easily convert a decimal to a percent by using a simple two-step method:

  • Step One: Multiply the Decimal Value by 100

    Multiplying a decimal by 100 is the same as moving the decimal point two places to the right.

  • Step Two: Write the Result as a Percentage.

In this step-by-step guide, we used this two-step method to make the following conversions from decimal to percent:

  • 0.5 = 50%

  • 0.36 = 36%

  • 0.08 = 8%

  • 0.045 = 4.5%

  • 1.39 = 139%

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How to Find Median in 3 Easy Steps

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How to Find Median in 3 Easy Steps

How to Find Median in Math Step-by-Step

Math Skills: How to find the median of a data set in 3 easy steps

 

Are you ready to learn how to find the median of a data set?

 

Finding the median of a data set is an important skill that will help you to analyze and make conclusions about data.

In math, the word median means middle and it refers to the middle number in a data set where the values are organized from smallest to largest.

In this Free Step-by-Step Guide on How to Find Median, you will learn how to find the median of a data set using a simple 3-step method, which we will practice and apply to several example problems. This guide will cover the following sections/topics:

You can click on any of the quick-links above to jump to any topic/section of this guide, or you can follow each section in order (we highly recommend this option if you are new to this topic).

Let’s begin!

 

Lesson Preview: How to find median in math in 3 easy steps.

 

What is the Median of a Data Set?

In statistics, a data set is a group of numbers that represent some form of data.

For example, consider a data set that represents the ages of 5 different students:

  • 12, 13, 15, 17, and 20

Note that a values in a data set can be represented as a list of numbers (as shown above) or contained with a set of curly brackets as shown below:

  • {12, 13, 15, 17, 20}

Note that both of these options represent the same data set, which, in this case, represents the ages of students.

Figure 01 below illustrates this data set and what the values represent.

 

Figure 01: This data set represents the ages of five different students.

 

In math, the median of a data set is the middle value of a set of data that is arranged in order from smallest to largest from left to right.

As long as the values in a data set are arranged in order of smallest to largest, you can simply locate the middle value to determine the median of the data set.

You can find the median, or middle, value of any data set by following these three simple steps:

  • Step One: List all of the numbers in order from smallest to largest

  • Step Two: Identify the middle number (if there are two middle numbers, continue to Step Three).

  • Step Three: If there are two middle numbers, find the average of the two numbers to determine the median.

Before we move onto any example problems of how to find the median of a data set, let’s apply these three steps to finding the median of the previously mentioned data set that represented the ages of five students as 12, 13, 15, 17, and 20.

Step One: List all of the numbers in order from smallest to largest

If we wanted to find the median of the data set that represented student’s ages, we would first have to make sure that the values are indeed in order from smallest to largest:

  • 12, 13, 15, 17, 20

It is easy to see that the numbers in the data set are arranged in order from smallest to largest.

Step Two: Identify the middle number (if there are two middle numbers, continue to Step Three).

  • 12, 13, 15, 17, 20

Step Three: If there are two middle numbers, find the average of the two numbers to determine the median.

In this case, the middle number is 15, so we can skip the third step and conclude that:

Final Answer: The median is 15.

Note that, later on in this guide, we will work through example problems where Step Three will be necessary.

The 3-step process for how to find median is displayed in Figure 02 below.

 

Figure 02: The median of a data set with values arranged in order from smallest to largest is the middle value.

 

Now that you are familiar with the concept of a median of a data set and what it represents, you are ready to gain some more practice with how to find median using our 3-step method.

How to Find Median Examples

How to Find the Median of a Data Set Example #1

Example: Find the Median of the Data Set:

Data Set: 3, 9, 11, 5, 17, 8, 16

Step One: List all of the numbers in order from smallest to largest

Notice that the numbers in our data set are not in order from smallest to largest. We can rewrite the data set so that the numbers are indeed in order as follows:

  • 3, 5, 8, 9, 11, 16, 17

Now that the numbers in our data set are arranged in order from smallest to largest, we are ready for our second step.

Step Two: Identify the middle number (if there are two middle numbers, continue to Step Three).

Since our data set has an odd number of values, we pinpoint one exact middle term, which, in this case, is 9:

  • 3, 5, 8, 9, 11, 16, 17

Step Three: If there are two middle numbers, find the average of the two numbers to determine the median.

In cases such as this, we can skip our third step and conclude that:

Final Answer: The median is 9.

Figure 03 below illustrates how we solved this first example step-by-step.

 

Figure 03: How to Find Mean Using 3 Easy Steps.

 

Notice that our data set for this first example has an odd amount of values (the data set had 7 total values). Whenever this is the case, you will be able to identify one single number and skip Step Three.

However, whenever there is an even amount of values, there will be two middle numbers and you will have to perform the third step to determine the median, which will be the case in the next example.

How to Find the Median of a Data Set Example #2

Example: Find the Median of the Data Set:

Data Set: 5, 14, 4, 9, 24, 16, 10, 18

Step One: List all of the numbers in order from smallest to largest

Our first step is to arrange all of the numbers in order from smallest to largest as follows:

  • 4, 5, 9, 10, 14, 16, 18, 24

Step Two: Identify the middle number (if there are two middle numbers, continue to Step Three).

Unlike the last example which had a data set with an odd amount of numbers, the data set in this example has an even amount of numbers (there are 8 total values).

In cases like this, when there is an even amount of numbers in the data set, there will be two middle numbers:

  • 4, 5, 9, 10, 14, 16, 18, 24

Notice that both 10 and 14 are both in the middle. Whenever there are two middle numbers, you will have to complete Step Three to determine the median of the data set.

Step Three: If there are two middle numbers, find the average of the two numbers to determine the median.

To find the median of a data set with two middle numbers, you simply have to find the average of the two numbers. You can do this by adding the two middle numbers together and then dividing by two as follows:

  • 10 + 14 = 24

  • 24 ÷ 2 = 12

Final Answer: The median is 12.

The step-by-step process for how to find a median of a data set with an even amount of values is shown in Figure 04 below.

 

Figure 04: How to Find Median of a Data Set with Two Middle Numbers.

 

Now that you are familiar with how to find median when a given data set has an odd amount of numbers or an even amount of numbers, let’s work through two more examples to further reinforce your understanding of how to find a median.

How to Find the Median of a Data Set Example #3

Example: Find the Median of the Data Set:

Data Set: 2, 58, 40, 17, 15, 16, 31, 6, 10, 18, 67, 23, 96

Step One: List all of the numbers in order from smallest to largest

First, rewrite the numbers as a list in order from smallest to largest:

  • 2, 6, 10, 15, 16, 17, 18, 23, 31, 40, 58, 67, 96

Step Two: Identify the middle number (if there are two middle numbers, continue to Step Three).

Notice that this particular data set has an odd amount of numbers (there are 13 total values). So, we can determine the middle value on the second step:

  • 2, 6, 10, 15, 16, 17, 18, 23, 31, 40, 58, 67, 96

Step Three: If there are two middle numbers, find the average of the two numbers to determine the median.

Since this data set had an odd amount of values, we were able to identify the median in Step Two and we can conclude that:

Final Answer: The median is 18.

Figure 05 below shows how we identified the median in Example #3.

 

Figure 05: How to Find a Median of a Data Set.

 

How to Find the Median of a Data Set Example #4

Example: Find the Median of the Data Set:

Data Set: 2, 9, 5, 8, 4, 10, 3, 15, 1, 25

Step One: List all of the numbers in order from smallest to largest

Just like the previous examples, we begin by rearranging the numbers in the data set so that they are in order from largest to smallest:

  • 1, 2, 3, 4, 5, 8, 9, 10, 15, 25

Step Two: Identify the middle number (if there are two middle numbers, continue to Step Three).

The data set in this Example #4 has an even amount of numbers (there are 10 total values).

Whenever there is an even amount of numbers in the data set, there will be two middle numbers:

  • 1, 2, 3, 4, 5, 8, 9, 10, 15, 25

Both 5 and 8 are in the middle, so we have to move onto Step Three to determine the value of the median.

Step Three: If there are two middle numbers, find the average of the two numbers to determine the median.

We can identify the median by finding the average of the two middle numbers as follows:

  • 5 + 8 = 13

  • 13 ÷ 2 = 6.5

Final Answer: The median is 6.5.

Notice that our final answer is a decimal, which is totally fine and quite common!

 

Figure 06: How to Find a Median Step-by-Step

 

Conclusion: How to Find Mean

Knowing how to find the median of a data set is an important and useful math skill that every student must learn.

The median of a data set that is arranged in order from smallest to largest is the middle value (i.e. median = middle).

You can find a median by applying the following three-step method:

  • Step One: List all of the numbers in order from smallest to largest

  • Step Two: Identify the middle number (if there are two middle numbers, continue to Step Three).

  • Step Three: If there are two middle numbers, find the average of the two numbers to determine the median.

Note that, for data sets with an odd amount of values, Step Three can be skipped. However, whenever a data set has an even amount of values, there will be two middle numbers and following Step Three will be necessary for finding the median value.

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How to Find Mode in Math—Explained

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How to Find Mode in Math—Explained

How to Find the Mode in Math Step-by-Step

Math Skills: How to find mode of a data set

 

Are you ready to learn how to find mode?

 

In math, it is important for students to understand different ways of measuring and describing central tendency when it comes to sets of data. One of the simplest ways to do this is a method called finding the mode, or most common number, of a given data set.

This free step-by-step guide on How to Find Mode will teach you everything you need to know about the mode of a set of numbers, how to find it, and what it represents.

You can use the links below to jump to any section of this guide, or you can work through each section in order.

Ready to get started?

 

Lesson Preview: How to find mode of a given data set.

 

What is the Mode of a Data Set?

In math, the term data set refers to a collection of values that represent some type of data.

For example, the amount of money in savings for five different students is $18, $21, $9, $13, and $21.

These dollar amounts can be expressed as a data set simply by writing the collection of numbers inside of curly brackets (separated by commas) as follows:

  • {18, 21, 9, 13, 21}

This scenario where we are using a data set to represent the savings of five students in illustrated in Figure 01 below.

 

Figure 01: How to Find Mode of a Data Set.

 

In math, the mode of a data set is the value that has the highest frequency. In other words, the mode is the value in the data set that is present more than any other number (i.e. the mode is the most common number).

Note that: a data set can have one mode, no mode, or multiple modes.

While finding the mode of a data set is a simple process, it is an important skill because it will help you to identify trends within a set of data and how it is distributed.

How to Find Mode

To find the mode of a data set, simply look at all of the values in the set and determine which value appears the most. Remember that a data set can have one mode, multiple modes, or no mode (we will see instances of all three scenarios in the examples below).

For example, how can we find the mode of the data set that represented student’s savings?

Remember that the data set included the following values:

  • {18, 21, 9, 13, 21}

In this case, notice that one value is present twice (21)), while all of the other values only occur once.

Therefore, we know that 21 is the most common number in the data set and we can conclude that:

Final Answer: The mode is 21.

The step-by-step process for how to find the mode in math are shown in Figure 02 below.

 

Figure 02: How to Find Mode: Carefully look for the most common value.

 

Now that you know what the mode of a data set represents and how to identify the mode, you are ready to work through several problems where you will gain more experience with identifying the mode of a given set of data.

How to Find the Mode Examples

How to Find the Mode Example #1

Example: What is the mode of the data set?

Data Set: 5, 2, 8, 2, 7, 3, 2

Remember that the mode of a data set is the value with the highest frequency (i.e. the value that occurs the most times).

Given the data set above, only one value occurs more than once, and that value is 2 (which occurs 3 times). So, we can conclude that the data set has a mode of 2.

Final Answer: The mode is 2.

Notice that the data set in this example has one, and only one, mode. Figure 03 below illustrates how to find the mode for this first example.

 

Figure 03: How to Find Mode of a Data Set.

 

Now that we have solved this first example, we can see that determining the mode of a given data set is relatively easy to do.

However, there are a few nuances to finding the mode as you will see in the next few examples.

How to Find Mode Example #2

Example: What is the mode of the data set?

Data Set: 14, 14, 17, 9, 11, 17, 24, 22, 17, 12

For this next example, it may be tempting to say that the mode of the data set is 14 since 14 occurs more than once. However, this is actually not the case. While it is true that 14 occurs twice in this data set, there is a number that occurs more than twice: 17 occurs 3 times.

Since 17 occurs more than any other number (it occurs 3 times), we can conclude that:

Final Answer: The mode is 17.

Just like the previous example, this data set has only one mode.

 

Figure 04: How to Find Mode in Math

 

How to Find Mode Example #3

Example: What is the mode of the data set?

Data Set: 5, 11, 9, 8, 9, 9, 11, 11, 7, 5, 11, 10, 9, 3, 11, 12

Notice that the given data set in this example is much larger than the data sets from the first two examples. In this case, we have several numbers that occur multiple times, so it would be helpful to make a quick tally chart for each value so we can accurately determine which value in this data set occurs the most:

  • 3: once

  • 5: 2 times

  • 7: once

  • 8: once

  • 9: 4 times

  • 10: once

  • 11: 5 times

  • 12: once

Now that we have logged the frequency of each value in the data set, we can see that the number with the highest frequency is 11 (it occurs 5 times).

Final Answer: The mode is 11.

Again, the data set in this example has only one mode.

 

Figure 05: How to Find Mode Explained.

 

How to Find Mode Example #4

Example: What is the mode of the data set?

Data Set: 5, 5, 5, 7, 7, 9, 9, 9, 7, 7, 9

Just like the last example, it is difficult to determine the mode of this data set simply by looking at it, so we will again create a tally chart to keep track of the frequency of each value:

  • 5: 3 times

  • 7: 4 times

  • 9: 4 times

Notice that this data set does not have one single value that occurs more than any other value. In fact, there is a “tie” in this case, where both 7 and 9 occur 4 times each in the data set.

In cases such as this, the data set can be considered multimodal, meaning that it has more than one mode (in this case, the data set has 2 modes).

Final Answer: The mode is 7 and 9.

 

Figure 06: Example of a multimodal data set (i.e. a data set that has more than one mode).

 

How to Find Mode Example #5

Example: What is the mode of the data set?

Data Set: 13, 0, 24, 83, 81, 55, 16, 42, 22

For this final example, we have a data set with nine values. We can track the frequency of each value as follows:

  • 0: once

  • 13: once

  • 16: once

  • 22: once

  • 24: once

  • 42: once

  • 55: once

  • 81: once

  • 83: once

Notice that each value in the data set only occurs once. In cases like this, we have a data set with no mode.

Final Answer: There is no mode.

 

Figure 07: Example of a data set that has no mode.

 

Conclusion: How to Find Mode

Understanding how to find the mode in math is a simple, yet important skill that will help you analyze and draw conclusions about sets of data.

In math, the mode of a data set is the value with the highest frequency (i.e. the value that occurs the most in the data set).

There are three ways to classify the mode of a data set:

  • One Mode: There is one value that occurs more than any other value in the data set.

  • Multimodal: There is more than one value that occurs the most (i.e. there is a “tie” for the highest frequency).

  • No Mode: Each value in the data set occurs only once.

With these nuances in mind, determining the mode of a data set is a pretty simple skill that all students can master with some study and practice.

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How to Find Mean in 3 Easy Steps

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How to Find Mean in 3 Easy Steps

How to Find the Mean in Math Step-by-Step

Math Skills: How to find the mean of a data set in 3 easy steps

 
 

Understanding how to find mean is an important and fundamental math skill that every student must learn at one point or another.

In math, the term mean is synonymous with average, meaning that the mean of a data set represents the average value of that data set.

This free guide will teach you the mathematical definition of mean and how to find the mean of a data set using a simple 3-step process. The following topics related to how to find mean will be covered:

While you can use the hyperlinks above to jump to any section of this guide, we highly recommend that you follow each section in order, starting with the first section below, where we will review the definition of mean and what it means in relation to a given data set.

Let’s get started!

 

Lesson Preview: How to find the mean in math in 3 easy steps.

 

What is the Mean of a Data Set?

In math, a data set is a collection or group of data in the form of numbers.

For example, consider the following data set which represents the saving amounts, in dollars, of five high school students:

  • $20, $25, $5, $25, and $15

These savings amounts can be expressed as a data set by removing the “$” signs and writing the numbers inside of curly brackets as follows:

  • {20, 25, 5, 25, 15}

This example of expressing the savings amounts of five high school students is illustrated in Figure 01 below.

 

Figure 01: What is a data set in math?

 

In math, the mean of a data set is one single value that represents the average of the entire data set.

In other words, the mean is a measure of central tendency (i.e. the average of a given data set). The mean can be found by taking the sum of all of the numbers in a data set and dividing that value by the total amount of data points.

So, you can find the mean of any data set by adding up all of the numbers and dividing that sum by the total amount of numbers in the data set.

How to Find Mean in 3 Easy Steps:

  • Step One: Add together all the numbers in the data set to find the sum.

  • Step Two: Determine how many numbers are in the data set.

  • Step Three: Divide the sum by the total amount of numbers in the data set to determine the mean.

To find the mean of the data set that represented student savings (as shown in Figure 01 above), we can simply follow these three steps to find the mean as follows:

Find the Mean of: {20, 25, 5, 25, 15}

Step One: Add together all the numbers in the data set to find the sum.

We can start by finding the sum of all of the numbers in the data set as follows:

  • 20 + 25 + 5 + 25 + 15 = 90

Step Two: Determine how many numbers are in the data set.

  • This particular data set has 5 numbers.

Step Three: Divide the sum by the total amount of numbers in the data set to determine the mean.

Finally, we just have to take our result from step one (the sum of all of the numbers in the data set) and divide it by the result of step two (the total number of numbers in the data set) as follows:

  • 90 ÷ 5 = 18

So, we can conclude that the average savings amount per student is $18.

Final Answer: The mean is 18.

The step-by-step process for how to find the mean in math are shown in Figure 02 below.

 

Figure 02: You can find the mean of any data set by adding up all of the numbers and dividing the sum by the total amount of numbers in the set.

 

Now that you understand what the mean of a data set represents and how to find it, let’s use our three-step process to solve three examples of how to find the mean of a data set.

How to Find the Mean of a Data Set

How to Find Mean Example #1

Example: Find the Mean of a Group of Siblings’ Ages

In this first example, we have a data set that represents the ages of six siblings with the following ages: 20, 22, 24, 26, 28, and 30.

So, our data set can be expressed as: {20, 22, 24, 26, 28, 30)

Step One: Add together all the numbers in the data set to find the sum.

Start by adding all of the numbers in the data set together as follows:

  • 20 + 22 + 24 + 26 + 28 + 30 = 150

Step Two: Determine how many numbers are in the data set.

  • The data set in this example has 6 numbers.

Step Three: Divide the sum by the total amount of numbers in the data set to determine the mean.

Now we are ready to find the mean by dividing the sum of all of the numbers by the total amount of numbers as follows:

  • 150 ÷ 6 = 25

Now we can conclude that the mean age of the siblings is 25 years old.

Final Answer: The mean is 25.

The entire step-by-step process for how to find the mean for this first example is illustrated in Figure 03 below.

 

Figure 03: How to Find Mean Using 3 Easy Steps.

 

As you can see from this first example, the process of finding the mean of a data set is an easy process that can be completed using just three steps.

The more that you practice using these steps on how to find mean, the easier these types of problems will become. Now, let’s move onto another example of how to find the mean of a data set.

How to Find the Mean in Math

How to Find Mean Example #2

Example: Find the Mean of a Data Set Representing Monthly Income

In this example, John has been tracking his monthly income and recorded the data in the following data set:

  • $1,200, $1,350, $1,250, $1,400, $1,300, $1,000, $900

For this example, we can make the values easier to work with by removing the dollar signs and expressing the values in a data set as follows:

  • {1200, 1350, 1250, 1400, 1300, 1000, 900}

Now we can use our 3-step process for how to find mean as follows:

Step One: Add together all the numbers in the data set to find the sum.

Just like the previous example, we can start by finding the sum of all of the numbers in the data set:

  • 1200 + 1350 + 1250 + 1400 + 1300 + 1000 + 900 = 8400

Step Two: Determine how many numbers are in the data set.

  • This data set has 7 numbers.

Step Three: Divide the sum by the total amount of numbers in the data set to determine the mean.

The last step is to divide the sum of all of the values in the data set by the total number of values in the data set:

  • 8400 ÷ 7 = 1,200

Finally, we can conclude that the mean monthly income is $1,200.

Final Answer: The mean is 1,200.

The process for finding the solution to this second example is shown in Figure 04 below.

 

Figure 04: How to Find the Mean of a Data Set.

 

Notice how our final answers in our first two examples ended up being whole numbers. This, however, will not always be the case. Now, let’s work through one more example where our final result will be a decimal.

How to Find the Mean of a Data Set

How to Find Mean Example #3

Example: Find the Mean of a Data Set Representing Student Test Scores

In this third example, we are looking to find the mean (or average) test score of a student with the following test scores: 78, 85, 92, 88, 80, 63, 90, 89, 71, and 95

Let’s go ahead and use our 3-step method for how to find mean of a data set to solve this problem and determine the mean test score.

Step One: Add together all the numbers in the data set to find the sum.

Our first step is to find the sum of all of the numbers in the data set:

  • 78 + 85 + 92 + 88 + 80 + 63 + 90 + 89 + 71 + 95 = 831

Step Two: Determine how many numbers are in the data set.

  • There are 10 values (or test scores) in this data set.

Step Three: Divide the sum by the total amount of numbers in the data set to determine the mean.

Finally, we just have to take our result from step one (831) and divide it by the total number of values in the data set (10) as follows:

  • 831 ÷ 10 = 83.1

Now we can make the conclusion that the student had an average test score of 83.1

Final Answer: The mean is 83.1

Notice how our result for this example was a decimal, which is totally fine!

Figure 05 below illustrates how we solved this third example.

 

Figure 05: How to Find Mean with Decimal Answers.

 

How to Find Mean Challenge

Challenge Problem

Scenario: On their last five science exams, students had the following scores:

  • Bonnie: 83, 100, 95, 61, 68

  • Celeste: 88, 83, 79, 86, 90

  • Michelle: 97, 64, 60, 89, 73

Which student had the highest mean test score?

For this challenge problem, you are tasked with determining which of the three students had the highest mean (or average) test score.

To solve this problem, you will have to calculate the mean test score of each student and then compare the means to see which on was the highest value.

 

Figure 06: Which student had the highest mean test score?

 

We can find the mean test score for each student by adding all five of their scores together and then dividing that sum by 5 as follows:

  • Bonnie: 83 + 100 + 95 + 61 + 68 = 407 → 407 ÷ 5 = 81.4

  • Celeste: 88 + 83 + 79 + 86 + 90 = 426 → 426 ÷ 5 = 85.2

  • Michelle: 97 + 64 + 60 + 89 + 73 = 393 → 393 ÷ 5 = 78.6

Now we can conclude that:

  • Bonnie’s mean test score was 81.4

  • Celeste’s mean test score was 85.2

  • Michelle’s mean test score was 78.6

And, we can conclude that Celeste’s 85.2 mean test score was the highest of the three students.

Final Answer: Celeste had the highest mean test score, which was 85.2.

 

Figure 07: How to Find Mean in Math: Test Scores

 

Conclusion: How to Find Mean

Knowing how to find the mean of a data set is an important math skill that every student should be familiar with.

In math, a data set is a collection of data values and the mean of a data set represents the average value of that set. You can find the mean of any data set by following the following three steps:

  • Step One: Add together all the numbers in the data set to find the sum.

  • Step Two: Determine how many numbers are in the data set.

  • Step Three: Divide the sum by the total amount of numbers in the data set to determine the mean.

Once you gain enough practice with finding the mean, you can simplify this process for how to find the mean by simply adding together all of the numbers in the data set and then dividing that sum by the total number of values.

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