Five Numbers, One Picture

Mathematics · Data & Statistics · ages 15-16

Name ______________________ Date ____________

A five-figure summary reads 6, 11, 14, 22 and 40. Where does the line inside the box go?
- at 14, the median
- at 23, halfway between the whisker tips
- at 22, the upper quartile
- at 11, the lower quartile
True or false: if the median line sits exactly halfway between Q1 and Q3, the middle 50% of the data is roughly symmetric.
Circle one: True False
A box plot has its box from 18 to 30, with whiskers reaching 10 and 44. What is the interquartile range?
Answer: ______________
A class's test scores have this five-number summary: minimum 40, Q1 55, median 68, Q3 80, maximum 95. What is the width of the box in the box plot (from Q1 to Q3)?
- 15
- 25
- 40
- 55
A box plot summarises 40 values. How many of them lie above the upper quartile?
Answer: ______________
A wider box means the data set contains more values.
Circle one: True False
Two box plots that look identical must have come from the same number of values.
Circle one: True False
Two box plots of delivery times: firm A's median is 20 minutes with an interquartile range of 6, and firm B's median is 32 with an interquartile range of 14. Which sentence compares them the way a report should?
- Plot A's box is further left and narrower than plot B's
- A's median is 20 and B's is 32, and A's interquartile range is 6 against B's 14
- Firm A delivers sooner than firm B and is far more predictable about it
- Plot A looks better than plot B
If the median line sits close to the left end of the box, the data is stretched out towards the higher values.
Circle one: True False
Class A's quiz scores have an IQR of 6 points. Class B's quiz scores have an IQR of 18 points. Which sentence correctly compares the two classes?
- Class A's scores are more consistent, clustering closer together than Class B's scores.
- Class B's scores are more consistent because 18 is a bigger number.
- Both classes have the same amount of spread in scores.
- IQR tells us nothing about how spread out scores are.

Answer key

For grown-ups. Fold this page away before handing over the rest.

Five Numbers, One Picture W1-mt_G_SnfEllzQ-s1

at 14, the median · The line inside the box marks the median, which is the middle figure of the five, 14. Halfway between the whisker tips is 23, and that is not what the line shows.
True · A median centered in the box means both halves of the middle data are about equally spread out.
12 · The box ends are the quartiles, so the interquartile range is 30 - 18 = 12. The whisker tips are the smallest and largest values and belong to the range instead.
25 · The box in a box plot always runs from Q1 to Q3, so its width is Q3 minus Q1.
10 · A quarter of the values sit above the upper quartile, and a quarter of 40 is 10. They are the ones drawn along the right whisker.
False · The box width is the interquartile range, a measure of spread. A box plot never shows how many values there are, so five readings and five thousand can give the same picture.
False · A box plot draws five numbers. Any two sets that share those five figures draw the same picture, whether one holds 14 values and the other holds 350.
Firm A delivers sooner than firm B and is far more predictable about it · A comparison has to land in the situation. The numbers and the shapes are the working; the reader wants what they mean for deliveries.
True · The quarter between the median and the upper quartile then covers much more ground than the quarter below the median, so the values thin out as they climb. That is a right skew.
Class A's scores are more consistent, clustering closer together than Class B's scores. · A smaller IQR means the middle 50% of scores are packed tighter together.