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?

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

Exercise

Go to your google classroom, and do the assignment individually