Averages and Range

Question 1

How do you find the mode of a set of data?

Answer 1

Mode means most common, so the mode of a set of data is the number that appears most often.

e.g. 1,8,3,4,6,1,8,8

The mode of the above list of numbers is 8.

Question 2

How do you find the mean of a set of data?

Answer 2

To find the mean, add all of the numbers together, then divide by the number of numbers.

‘Don’t be mean, add them up and share them out!’

e.g. 1, 4, 2, 3, 1, 3, 7

1 + 4 + 2 + 3 + 1 + 3 + 7 = 21

21/3 = 7

Question 3

How do you find the range of a set of data?

Answer 3

The range is the biggest number minus the smallest number.

e.g. 2, 4, 6, 3, 1, 6, 4, 4, 9

The range is 9 - 1 = 8

Question 4

How do you find the median of a set of data?

Answer 4

The median is the middle number when the data are listed in order. If there are two ‘middle numbers’, add them together and divide by 2.

e.g. 1, 5, 3, 7, 5, 9, 3, 6, 5

In order, the list is 1, 3, 3, 5, 5, 5, 6, 7, 9

so the median is 5.

Question 5

Find the mode of this set of data.

8, 6, 9, 11, 10, 11, 7, 8, 6, 9, 11

Answer 5

The mode is 11 because it appears in the list most often.

Question 6

Find the mean of this set of data to one decimal place.

8, 6, 9, 11, 10, 11, 7, 8, 6, 9, 11

Answer 6

Add the numbers together and divide by 11 since there are 11 numbers in the list.

The mean is 8.7 to one decimal place.

Question 7

Find the range of this set of data.

8, 6, 9, 11, 10, 11, 7, 8, 6, 9, 11

Answer 7

The range is 11 - 6 = 5

Question 8

Find the median of this set of data

8, 6, 9, 11, 10, 11, 7, 8, 6, 9, 11

Answer 8

In order: 6, 6, 7, 8, 8, 9, 9, 10, 11, 11, 11

So the median (middle number) is 9.

Question 9

Find the mode(s) of this set of data.

15, 22, 17, 11, 39, 28, 56, 8, 15, 34, 17

Answer 9

There are two modes: 15 and 17.

Question 10

Find the mean of this set of data.

12, 15, 22, 17, 11, 39, 44, 28, 56, 71, 8, 15, 22, 34, 17

Answer 10

The sum of the numbers is 411, and there are 15 numbers in the list.

The mean is 411/15 =27.4.

Question 11

Find the range of this set of data.

12, 15, 22, 17, 11, 39, 44, 28, 56, 71, 8, 15, 22, 34, 17

Answer 11

The range is 71 - 8 = 63

Question 12

Find the median of this set of data.

12, 15, 21, 17, 11, 39, 44, 28, 56, 71, 8, 15, 22, 34, 17

Answer 12

In order: 8, 11, 12, 15, 15, 17, 17, 21, 22, 28, 34, 39, 44, 56, 71

There are two ‘middle numbers’ so we find their mean.

The median is (21 +22)/2 = 21.5