Question

The following data represent weights in kilograms of maize harvest from a random sample of 72 experimental plots on St. Vincent, an island in the Caribbean (Reference: B. G. F. Springer, Proceedings, Caribbean Food Corps. Soc., Vol. 10, pp. 147-152). For convenience, the data are presented in increasing order.

7.8 9.1 9.5 10.0 10.2 10.5 11.1 11.5 11.7 11.8
12.2 12.2 12.5 13.1 13.5 13.7 13.7 14.0 14.4 14.5
14.6 15.2 15.5 16.0 16.0 16.1 16.5 17.2 17.8 18.2
19.0 19.1 19.3 19.8 20.0 20.2 20.3 20.5 20.9 21.1
21.4 21.8 22.0 22.0 22.4 22.5 22.5 22.8 22.8 23.1
23.1 23.2 23.7 23.8 23.8 23.8 23.8 24.0 24.1 24.1
24.5 24.5 24.9 25.1 25.2 25.5 26.1 26.4 26.5 26.7
27.1 29.5

a) Compute the five-number summary.
b) Compute the interquartile range.
c) Make a box-and-whisker plot.
d) Discuss the distribution. Does the lower half of the distribution show more data spread than the upper half?

Answer 1

See explanation

Explanation:

7.8 9.1 9.5 10.0 10.2 10.5 11.1 11.5 11.7 11.8

12.2 12.2 12.5 13.1 13.5 13.7 13.7 14.0 14.4 14.5

14.6 15.2 15.5 16.0 16.0 16.1 16.5 17.2 17.8 18.2

19.0 19.1 19.3 19.8 20.0 20.2 20.3 20.5 20.9 21.1

21.4 21.8 22.0 22.0 22.4 22.5 22.5 22.8 22.8 23.1

23.1 23.2 23.7 23.8 23.8 23.8 23.8 24.0 24.1 24.1

24.5 24.5 24.9 25.1 25.2 25.5 26.1 26.4 26.5 26.7

27.1 29.5

A. The five-number summary is

• Minimum = 7.8
• Maximum = 29.5
• Median
  `=(20.2+20.3)/(2)=20.25`
• 
  `Q_1=(14.0+14.4)/(2)=14.2`
• 
  `Q_3=(23.8+23.8)/(2)=23.8`

B. The interquartile range is

`Q_3-Q_1=23.8-14.2=9.6`

C. See attached diagram

D. The distribution is not symmetric, the left half shows more data than the right part