Cumulative Frequency

Frequency Distribution

Cumulative Frequency

Learning Objectives

• Calculate cumulative frequencies

• Plot and draw cumulative frequency curves

• Interprete cumulative frequency curves

• Use cumulative frequency to estimate the median​

Cumulative frequency column

• The cumulative frequency, cf, gives the number of scores equal to or less than that score.

• The number of times a data value occurs is its FREQUENCY.

Example 1: Score of 10 students

• How many students scored 7 or less?

• How many students scored 8 or less?

• How many students scored 9 or less?

Multiple Choice

How many students are there altogether?

• 1

• 3

• 30

Multiple Choice

How many students scored 20 or less?

• 3

• 7

• 10

Multiple Choice

How many students scored 30 or less?

• 7

• 13

• 23

Multiple Choice

How many students scored between 10 and 30?

• 7

• 13

• 20

Multiple Choice

How many students scored greater than 30?

• 13

• 7

• 6

Cumulative frequency nonsense

• You cannot have a cumulative frequency for categorical data.

• For instance, when recording the number of different coloured cars in a parking area it would be nonsense to say there were 13 cars which were blue or less.

Cumulative frequency for grouped data

• A cumulative frequency graph shows the total number of pieces of data up to and including a particular value.

Rules for construction

• Plot the highest value in each class interval along the horizontal axis.

• Plot the cumulative frequency on the vertical axis.

• Join up the points to give a smooth curve.

Example 2

This table shows the heights of some sunflowers.

Reading a cumulative frequency graph

• Each point plotted shows you the cumulative frequency up to and including that value.

• The increase in cumulative frequency between each point tells you the frequency of that class interval.

Data are above a particular value

• For example, how many sunflowers were taller than 190 cm?

• This tells you how many sunflowers  were less than or equal to 190 cm.

• Subtract the cumulative frequency from the total frequency. 30 – 23 = 7

Multiple Choice

How many students are there altogether?

• 80

• 76

• 6

Multiple Choice

How many students took up to 20 seconds?

• 6

• 26

• 80

Multiple Choice

How many students took up to 40 seconds?

• 6

• 20

• 29

Multiple Choice

How many students took between 20 and 40 seconds

• 6

• 20

• 26

Multiple Choice

How many students took above 1 minute?

• 62

• 18

• 80

Exercise

Go to your google classroom, and do the assignment individually