En anglais

Five numbers and what they tell you

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
A summary has minimum 6, Q1 11, median 11, Q3 19 and maximum 25. Its median line may coincide with the lower end of its box.
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 score summary is minimum 42, Q1 57, median 69, Q3 82, maximum 96. Which described feature corresponds to the interval from 69 to 82?
- the lower whisker
- the upper part of the box
- the lower part of the box
- the upper whisker
There are 40 distinct ordered values. Use medians of the lower and upper halves for quartiles. How many observations are strictly above Q3?
Answer: ______________
A wider box means the data set contains more values.
Circle one: True False
A bare five-number summary identifies every gap between consecutive observations.
Circle one: True False
Firm A's delivery-time median is 20 minutes and its IQR is 6. Firm B's median is 32 minutes and its IQR is 14. Which comparison is supported?
- A is typically slower, with more central variation.
- A is typically quicker, with more central variation.
- A is typically quicker, with less central variation.
- A is typically slower, with less central variation.
If all five summary values are symmetrically spaced about the median, the complete observation list must be symmetric.
Circle one: True False
Class A's score IQR is 6 points and B's is 18 points. Every score in both classes is multiplied by 3. What are the resulting IQRs?
- A: 18 points; B: 18 points
- A: 18 points; B: 54 points
- A: 6 points; B: 54 points
- A: 6 points; B: 18 points

Answer key

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

Five numbers and what they tell you 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 · Q1 and the median both equal 11. Their described positions therefore coincide. Equal summary values are allowed.
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.
the upper part of the box · 69 is the median and 82 is Q3. The interval from the median to Q3 is the upper part of the described box.
10 · The upper half occupies positions 21 to 40. Its median averages positions 30 and 31. With distinct values, Q3 lies strictly between those observations, leaving positions 31 to 40 above it: ten observations.
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 · The five summary values do not list all observations. Different observations between the quartiles can preserve the summary while producing different gaps.
A is typically quicker, with less central variation. · A's median is 12 minutes shorter, and its IQR is 8 minutes smaller. A has the shorter median delivery time and less central variation. These summaries do not establish maximum delays or overall reliability.
False · The list 0, 2, 3, 5, 8, 8, 10 has summary 0, 2, 5, 8, 10 under the stated median-of-halves convention. The summary is symmetric about 5, but the observation 3 has no matching 7.
A: 18 points; B: 54 points · A positive scaling factor multiplies each quartile and their difference. The new IQRs are 3 × 6 = 18 and 3 × 18 = 54 points.