Mode, Median and Range

Aim:

To find the mode, median and range, and the modal class for grouped data.

Put these numbers in numerical order with the smallest first.

7, 3, 9, 2, 10, 8, 5, 4, 14, 12

2, 3, 4, 5, 7, 8, 9, 10, 12, 14,

34, 67, 38, 19, 44, 57, 24, 31, 62, 20

19, 20, 24, 31, 34, 38, 44, 57, 62, 67

2, -3, 1, 4, -4, 0, 5, -2

-5

1-4 -3 -2 0 2 4 5

-4 -3 -2 -1 0 2 3 4 51

Averages

An average is a useful statistic because it represents a whole set of values by just a single or typical value.

• Where have you heard the word average before?

• Where have you seen it used?

The Mode

The mode is a type of average The mode is the value that occurs most

often in a set of data

Example

5, 6, 8, 2, 4, 5, 3, 5 MODE = 5

Sometimes there is no mode because either all the values are different, or no single value occurs more often than other values

What letter does your first name begin with?

What is the mode first letter for a name in class 7Y2?

THE MODE DOESN’T HAVE TO BE A NUMBER

Mode, Median and Range

Aim: To find the mode, median and range, and the modal class for grouped data.

PAGE 52

EXERCISE 5A

QUESTION 1

THE MODE

The Median

The median is another type of averageThe median is the middle value for a set of

data when the values are put in numerical order.

Example

6, 8, 3, 7, 5, 2, 4 in order 2, 3, 4, 5, 6, 7, 8

Median = 5For an odd number of values in data set, there is only one middle value.

This is the median.

What is the median test score for the following set of results?

5, 7, 7, 8, 10, 12, 14, 15

For an even number of values in a data set, there are two middle values.

The median is the value in the middle of these two values.

Median = 9

The median

PAGE 51

EXERCISE 5A

QUESTION 2

The Range

The range is not an average.The range of a set of data is the largest

value minus the smallest value.It shows how the data is spread out.

A small range shows that the values in a set of data are similar in size

A large range shows that the values differ considerably

Find the range:

What number month were you born in?

Range = Largest number – smallest number

Range =

What does this tell us about the birthdays of class 7Y2?

For example, January = 1, June = 6, and December = 12

The Range

PAGE 51

EXERCISE 5A

QUESTION 3

Modal ClassFor grouped data such as the example below, we cannot find the mode.

Time (Mins.) Frequency

0-2 2

3-5 4

6-8 3

9-11 1

Instead, we find the MODAL CLASS. This is the group that occurs most often.

Modal class = 3-5

Why isn’t it possible to calculate an exact mode or median from grouped data?