Box plots

The Maths Habit

Jo and Max each throw five darts.

Jo: 18, 20, 19, 21, 22
Max: 5, 38, 12, 35, 10

Who would you pick for your team? Why?

Either, with a reason: Jo is steady, Max is not

Interquartile range
Upper quartile take away lower quartile: the spread of the middle half of the data.

What is the interquartile range?

Lower quartile 20, upper quartile 34 14

What is the range?

Lowest 12, highest 44 32

  1. The lower quartile is 15 and the upper quartile is 27. Find the interquartile range.

    12

  2. The lowest value is 3 and the highest is 41. Find the range.

    38

  3. The lower quartile is 38 and the interquartile range is 20. Find the upper quartile.

    58

Distances run (km), in order:
4, 7, 11, 13, 15, 17, 19, 20, 22, 27, 33
Which value cuts them into two halves?

05101520253035Distance (km)Median 17

17: five values below it, five above

Now cut each half in two.
Where are the cuts?

05101520253035Distance (km)MedianLower quartileUpper quartile

11 and 22: two values in each quarter

The box is the middle half.
The whiskers reach the lowest and the highest.

05101520253035Distance (km)LQMedianUQ

A box plot needs only five numbers:
lowest, LQ, median, UQ, highest.

Draw a box plot for the table.

LowestLQMedianUQHighest
Distance411172233
05101520253035Distance (km)
Interquartile range11

Draw a box plot for the table.

LowestLQMedianUQHighest
Age2331364458
202530354045505560Age (years)
Interquartile range13

Draw a box plot for the table.

LowestLQMedianUQHighest
Distance411172233
05101520253035Distance (km)
Interquartile range11

Draw a box plot for the table.

LowestLQMedianUQHighest
Score1226303846
101520253035404550Score
Interquartile range12

  1. What percentage of the data is below the upper quartile?

    75%

  2. One value is far bigger than the rest. Which changes more: the range or the interquartile range?

    The range

Box plots worksheet, page 1

Answer sheet

  1. Class A has median 52 and interquartile range 10. Class B has median 47 and interquartile range 22. Which class is more consistent?

    Class A

  2. A box plot has lowest 10, lower quartile 18, median 24, upper quartile 30 and highest 60. Which quarter is most spread out?

    The top quarter

  1. Lowest 6, lower quartile 14, median 22, upper quartile 31, highest 40. Find the interquartile range.

    17

  2. Lowest 5, LQ 12, median 16, UQ 21, highest 28. Draw a box plot.

    Box 12 to 21, median 16, whiskers 5 and 28
    051015202530

  3. Interquartile range: class A 9, class B 20. Which class is more consistent? Why?

    A: smaller spread
Exit tickets to print