Median and quartiles from a graph

The Maths Habit Handout to print

  1. The frequencies of four classes are 4, 9, 12 and 5. Work out the cumulative frequencies.

    4, 13, 25, 30
  2. The class 150 < h ≤ 160 has a cumulative frequency of 27. Which point is plotted?

    (160, 27)
  3. The cumulative frequencies of four classes are 3, 11, 24 and 30. Find the frequency of the third class.

    13

40 people stand in a queue.

Who is in the middle of the queue? Who is a quarter of the way along?

About the 20th person; about the 10th

Lower quartile
A quarter of the way through the data.
Upper quartile
Three quarters of the way through the data.
Interquartile range
Upper quartile take away lower quartile.

¼of the way up: lower quartile½of the way up: median¾of the way up: upper quartile

There are 80 values.
How far up is the median?

40

There are 80 values.
How far up is the upper quartile?

60

There are 40 values.

how far upread acrossLower quartile10→20Median20→35Upper quartile30→45Interquartile range25

There are 60 values.

how far upread acrossLower quartile15→160Median30→165Upper quartile45→170Interquartile range10

There are 40 values.

how far upread acrossLower quartile10→20Median20→35Upper quartile30→45Interquartile range25

There are 80 values.

how far upread acrossLower quartile20→20Median40→30Upper quartile60→35Interquartile range15

There are 40 values. How many are more than 30?

Cumulative frequency worksheet, page 2

Answer sheet

  1. Class A has a median of 52 and an interquartile range of 10. Class B has a median of 47 and an interquartile range of 21. Compare the two classes.

    A scored higher and was more consistent
  2. 40 runners finish a race. 10 of them take more than 50 minutes. Which quartile is 50 minutes?

    The upper quartile

  1. The graph shows the times of 40 runners. Find the median time.

    25 minutes
    010203040Cumulative frequency0102030405060Time (minutes)
  2. Find the interquartile range.

    15 minutes
  3. How many runners took more than 40 minutes?

    6
Exit tickets to print