How to Find the Mode of a Set of Numbers

Finding the Range: Interactive Questions

example of how to find the range

The range is the difference between the biggest and smallest numbers in a list.

To find the range, subtract the smallest number in a list from the largest number.

The largest number is 9.

The smallest number is 2.

9 – 2 = 7 and so, the range of these numbers is 7.

The larger the range, the more spread out a set of numbers is.

To find the range of a list of numbers, subtract the smallest number from the largest number.

example of finding the range of a set of numbers

To find the range, subtract the smallest number from the largest number.

The largest number is 15.

The smallest number is 5.

It does not matter that there are two 5’s in the list, we still use 5 as the smallest value.

15 – 5 = 10 and so, the range of these numbers is 10.

Supporting Lessons

Finding the Range Activity

Finding the Range Worksheets and Answers

Finding the Range

How to Find the Range of a List of Numbers

To find the range of a list of numbers follow these steps:

Find the biggest number in the list.

Find the smallest number in the list

Subtract the smallest number from the biggest number.

This answer is the range.

Here are some examples of finding the range of a list of numbers.

In this example we have the list: 4, 5, 7, 9, 3, 6, 2, 4.

The first step is to find the biggest number in the list, which is 9.

The second step is to find the smallest number in the list, which is 2.

The third step is to subtract the smallest number from the biggest number.

example of finding the range of a list of numbers

9 – 2 = 7 and so, the range of these numbers is 7.

Here is a different example of calculating the range.

In this example we have the list: 11, 15, 9, 5, 11, 6, 5, 8.

To find the range, we subtract the smallest number from the largest number.

The largest number is 15 and the smallest number is 5.

It does not matter if there are many of the same number in the list. For example, in this case there are two 5’s. It does not matter because 5 is still the smallest number.

example of calculating the range

15 = 5 = 10 and so, the range of these numbers is 10.

What is the Range Used For?

The range is a number that is used to indicate how spread out a set of numbers are. The range is the biggest number subtract the smallest number so it tells us how far apart the biggest number and the smallest number are. The range is used to compare different lists of numbers.

The bigger the range, the more spread out the biggest and smallest numbers are.

The smaller the range, the less spread out the biggest and smallest numbers are.

Here are two different lists. We will calculate the range for both examples.

In this list, the largest number is 9 and the smallest number is 2. 9 – 2 = 7 and so the range is 7.

The largest number is 9 and the smallest number is 2 so the range is 9 - 2 which is 7

In this next list, the largest number is 15 and the smallest number is 5. The range is 15 – 5 = 10.

The largest number is 15 and the smallest number is 5 so the range is 15 - 5 which is 10 width=

The range can be used to compare the two lists. The range of list 1 was 7 and the range of list 2 was 10.

The numbers in list 1 might be less spread out than the numbers in list 2 because the range of list 1 is smaller than the range of list 2.

The range only takes into account the smallest and largest numbers and so, we cannot describe the spread of the entire list using the range. However it is a very simple way to measure how spread out the numbers in each list are.

Now try our lesson Ordering Numbers to 100 where we learn how to put numbers in order from smallest to largest.

Ordering Numbers to 100

ordering numbers

Finding the Mode

How to Find the Mode

Finding the Mode: Interactive Question Generator

example of finding the mode of a set of numbers

This set of numbers is: 5, 2, 7, 5, 5, 5, 1, 2, 0.

The mode is the number that appears the most.

It is easier to see the mode by putting the numbers in order from smallest to largest.

In order, the numbers are: 0, 1, 2, 2, 5, 5, 5, 5, 7.

The most frequent number is 5.

There are four number fives.

5 is the mode.

The mode is the most frequent number in a set of data.

The mode is the number that appears the most.

example of finding the Mode of a set of numbers

We will find the mode of the set of numbers: 3, 1, 7, 1, 1, 9, 4, 2, 9, 6, 0, 9.

We begin by writing the numbers in order from smallest to largest.

We have: 0, 1, 1, 1, 2, 3, 4, 6, 7, 9, 9, 9.

There are three 1’s and also three 9’s.

The most common number is both 1 and 9.

We say that the mode is 1 and 9. We have two modes in this example.

Data that has two modes is called bimodal.

Supporting Lessons

Counting to 10 on a Number Line

[

Finding the Mode Interactive Questions

Finding the Mode Worksheets and Answers

How to Find the Mode of a Set of Numbers

The mode is the most frequent value in a data set. It is the number that appears the most.

To find the mode of a set of numbers use the following steps:

Count how many of each number there are in total.
The mode is the number that appears the most.
If there is more than one of these numbers, then they are all the mode.
If all of the numbers appear in equal amounts then there is no mode.

When there are only a small amount of numbers in the list, it can be easiest to count the numbers in the list immediately.

However, for larger lists of numbers, we can first write the list of numbers in order from smallest to largest. This can help us to count how many of each number there are.

Here is an example of finding the mode from a list of numbers.

We have: 5, 2, 7, 5, 5, 5, 1, 2, 0.

We can write the numbers in order as:

0, 1, 2, 2, 5, 5, 5, 5, 7.

When rewriting the numbers in order, you need to make sure that you have written all of the numbers once. It can help to cross numbers off the original list as you rewrite them.

You should also count how many numbers there were to begin with and count how many are in your rewritten list.

Here there were 9 numbers in total and in the rewritten list, we have 9 numbers.

The mode is 5 as it appears the most frequently

From the list of: 0, 1, 2, 2, 5, 5, 5, 5, 7 we can count the amount of each number.

We can see that there are two 2’s and four 5’s.

5 is the number that appears the most and so, 5 is the mode.

example of finding the mode of a set of numbers

In this example, we have a large list of numbers.

We have 12 numbers: 3, 1, 7, 1, 1, 9, 4, 2, 9, 6, 0, 9.

To find the most of this list of numbers, we first write the numbers in order.

In order from smallest to the largest, the numbers are:

0, 1, 1, 1, 2, 3, 4, 6, 7, 9, 9, 9.

We can count these numbers to check that we wrote all 12 numbers.

The modes are 1 and 9 as they both appear the most frequently in the list

In this example, the most common numbers are both 1 and 9.

There are three 1’s and three 9’s.

We say that the data is bimodal. Bimodal means that there are exactly two modes.

If the data is bimodal we write them both as our answer. We do not average the modes.

example of finding the mode from a list in bimodal data

This data was bimodal so we wrote both 1 and 9 as our mode.

If there are many modes, then we can call the data multimodal.

If every single number appears the exact same amount of times, then we say the data does not have a mode.

Now try our lesson on How to Find the Range where we learn what the range of a set of numbers is.

How to Find the Range

range

Median of an Even Set of Numbers

how to find the median of an even set of numbers example

To find the median, put the numbers in order and then find the number in the middle.

First we arrange the numbers in
ascending orderStarting with the smallest number and getting larger.
to get: 1, 3, 4, 6, 7 and 9.

We cross off the same amount of numbers at each end of the list until two numbers remain in the middle.

The median is the value in the middle of these remaining two numbers.

5 is the median as it is exactly in between 4 and 6.

We can also add the two numbers and then divide this by 2 to get the median.

4 + 6 = 10 and 10 ÷ 2 = 5.

Write the list of numbers in order from smallest to largest and cross off numbers at each end.

Add the two middle numbers and divide this by 2 to get the median.

example of finding the median of an even amount of numbers

We arrange our numbers in
ascending orderStarting with the smallest number and getting larger.
to get: 0, 3, 4, 6, 7, 7, 8 and 9.

We cross off the numbers at each end until only two numbers remain: 6 and 7.

The median is exactly in between 6 and 7, so the median is 6.5.

We could also add 6 and 7 to make 13 and then halve 13 to get the median of 6.5

Supporting Lessons

Finding the Median

Median of an Even Set: Interactive Activity

Median of an Even Set of Numbers Worksheets and Answers

median of an even set of numbers worksheet PDF

Median of an Even Set

How to Find the Median from an Even Amount of Numbers

To find the median from an even amount of numbers:

Write the list of numbers in order from smaller to largest.

Cross off the same amount of numbers at each end of this ordered list until two numbers remain in the middle.

Add these two numbers together and divide the result by 2 to get the median.

We can say that the Median is the middle number in an ordered set of values.

Definition of the median

The first step to find the median is to put the numbers in order from smallest to largest.

It is important to make sure that we have the same amount of numbers in the rewritten, ordered list as we did in the original list.

Writing an even set of numbers in ascending order before finding the median

The list of “6, 3, 1, 7, 4, 9” becomes “1, 3, 4, 6, 7, 9”.

Now that the numbers are in order, starting with the smallest and ending with the largest, we can find the middle value.

To find the middle value, we cross off the same amount of values at the beginning and end of our list of numbers.

We can cross off 2 numbers at the beginning of our list: 1 and 3.

And we can also cross off 2 numbers at the end of our list: 7 and 9.

We need to cross off the same amount of numbers at each end.

To find the median of an even set of numbers, cross off at each end and then find the mean of the two remaining numbers

There are two numbers remaining in the centre: 4 and 6.

If we crossed off another number at each end we would end up crossing out both the 4 and the 6 and all of the numbers would be crossed off.

Therefore when finding the median from an even amount of numbers, we will always stop crossing off numbers to leave two numbers remaining in the middle.

To find the median from these two remaining numbers, we need to find the number that is halfway between 4 and 6.

5 is directly between 4 and 6 and therefore 5 is our median value.

Finding the median with an even amount of numbers example

It was easy to see that 5 was directly between 4 and 6.

However if the numbers are more spread apart, the median is not as obvious. <> There is an alternate method to find which value is in the middle of two numbers:

Add the two numbers.
Divide this result by two.

For example, to find the number in between 4 and 6, we add 4 and 6 to get 10 and then divide 10 by 2 to get 5.

5 is directly between 4 and 6 and is the median of the list.

Teaching Finding the Median with an Even Set

Here is another example of finding the median from an even set of numbers.

When teaching finding the median, it is important to remember to put the list of numbers in order from smallest to largest.

This step is commonly forgotten and it is the first thing to check if you are not arriving at the correct answer.

In this example, the list “8, 7, 6, 7, 3, 9, 0, 4” becomes “0, 3, 4, 6, 7, 7, 8, 9”.

After reordering the list, it is worth checking that there are the same amount of numbers in each list. If we have missed out a number, then the answer will be wrong.

We check that there are 8 numbers in total in each list.

Example of finding the median in an even set of numbers

When there is an even amount of numbers, we cross off numbers at each end to leave two numbers in the middle.

We will always leave two numbers in the middle.

We have 0, 3, 4, 6 , 7, 7, 8, 9.

We have two numbers remaining: 6 and 7.

Because 6 and 7 are

, it is easy to find the halfway value.

6.5 is halfway between 6 and 7 and so, 6.5 is the median.

We simply put a the .5 after the smaller number. 6.5 is 6 and a half.

Alternatively, we can add 6 and 7 and then divide this by 2.

6 plus 7 equals 13 and half of 13 is 6.5.

Now try our lesson on Finding the Mode where we learn what the mode of a list of numbers is.

Finding the Mode

mode

Finding the Median

Finding the Median: Interactive Questions

how to find the median

The median is a type of average.

The median is the middle number in an ordered list of numbers.

We first put the list of numbers in order from smallest to largest.

The median is the middle number in this ordered list.

To find the middle number, cross off a number on both the left and right of the list.

Cross off numbers at each end of the list until only one number remains.

The median is middle number in a list that has been put in order from smallest to largest.

finding the median of a list of numbers

The median is the middle number in an ordered list of numbers.

We first write the 7 numbers in order from smallest to largest.

The list 7, 9, 0, 1, 3, 4, 1 is written in order as 0, 1, 1, 3, 4, 7, 9.

We check that there are 7 numbers in the new ordered list so that we know that we haven’t missed any out.

We now cross off numbers at each end of the list until one remains in the middle.

3 is the median of this list of numbers.

Supporting Lessons

Finding the Median Activity

Finding the Median Worksheets and Answers

Median of an Even Set of Numbers

Finding the Median

What is the Median?

The median is a type of average. The median is the middle value in an ordered list of numbers. Simply put, there are the same amount of numbers that are less than the median as there are numbers larger than the median.

For example, here is an unordered list of numbers. We first write them in order from smallest to largest.

Rewriting numbers in ascending order

The median is the middle number in this ordered list.

crossing off numbers at each end to find the median

The median is 4.

We can see that there are 2 numbers less than 4 and 2 numbers more than 4. The median is exactly in the middle of the data.

How to Calculate the Median

To calculate the median use the following steps:

Write the numbers in order from smallest to largest.

Cross off a number at each end of the list.

Keep crossing off numbers until only one number remains.

If one number remains, this is the median.

If two numbers remain, add the numbers and divide by 2 to find the median.

Here is an example of calculating the median of a list of numbers.

We have the list of numbers: 5, 2, 1, 7, 4.

The first step is to write them in order from smallest to largest.

There are 5 numbers in the original list and so, there should still be 5 numbers in the reordered list.

putting a list of numbers in order

Putting the list in order, we have: 1, 2, 4, 5, 7. This is still 5 numbers in total so we know that we haven’t missed any out.

When teaching the median, we should remember to count the numbers in the each list as it is a common mistake to miss out a number when reordering longer lists.

The next step is to cross off numbers at each end of the list until only one number remains.

We cross off 1 and 7 together and then 2 and 5 together.

finding the median of an ordered list of numbers

We can see that the middle number of 1, 2, 4, 5, 7 is 4.

The median of the list of numbers is 4.

Here is an animation showing the complete process of finding the median.

how to find the median

Here is another example of finding the median of a list of numbers.

We have the list of numbers: 7, 9, 0, 1, 3, 4, 1.

The first step is to put the numbers in order making sure that there are still the same amount of numbers in the original list as there are in the reordered list.

It is also useful to identify any duplicate numbers. There are two 1’s in our list, so there should be two 1’s in the reordered list.

ordering a list of numbers from smallest to largest

The list in order from smallest to largest is 0, 1, 1, 3, 4, 7, 9.

There are 7 numbers in the original list and in the new reordered list, so it is likely that we haven’t missed any numbers out.

We now cross off numbers from each end of the list.

example of finding the median from an ordered list

We cross off numbers at each end until only one number remains.

We can see that in this list: 0, 1, 1, 3, 4, 7, 9 that 3 is the number left in the middle.

3 is the median of this list of numbers.

We can see that there are 3 numbers less than the median and 3 numbers more than the median.

Here is an animation showing how to find the median of this list of numbers.

example of finding the median of a list of numbers

Finding the Median with an Even Set of Numbers

If there is an even amount of numbers in the list, then two numbers remain when numbers are crossed off at each end of the list. Add these two numbers and divide the result by two to find the median.

For example here is the list: 1, 3, 4, 6, 7, 9.

There are 6 numbers, which is an even amount.

If we cross off a number at each end we have: 1, 3, 4, 6, 7, 9.

If we cross off another number at each end we have: 1, 3, 4, 6, 7, 9.

There are two numbers remaining.

If we cross off another two numbers, then all of the numbers would be crossed out.

median of an even set of numbers

The two numbers remaining are 4 and 6.

The median is found by adding the two numbers and then dividing by 2.

4 + 6 = 10 and 10 ÷ 2 = 5.

The median is 5. 5 is directly in between 4 and 6.

To look at further examples of finding the median of an even set of numbers in more detail, look at our next lesson.

Now try our lesson on Median of an Even Set of Numbers where we learn how to find the median when we have an even amount of numbers.

median of an even set of numbers

How to Find the Mean

Calculating the Mean: Interactive Question Generator

how to teach the mean of a set of data

The mean is an average.

We will find the average number of counters in these 3 groups.

To find the mean, we add up the numbers to find the total.

2 + 4 + 3 = 9.

We now share the counters out equally between the 3 groups.

9 ÷ 3 = 3

The mean number of counters is 3.

To find the mean we add the numbers up and divide this total by how many numbers there are.

Steps to Find the Mean of a set of numbers

To find the mean of a set of numbers, add the numbers and divide by how many numbers there are.

Adding the numbers we have: 2 + 4 + 3 = 9.

There are 3 numbers in total, which are ‘2’, ‘4’ and ‘3’.

9 ÷ 3 = 3.

The mean of the numbers is 3.

Supporting Lessons

Calculating the Mean Interactive Questioms

Finding the Mean Worksheets and Answers