Question

The box plot shows information

about the heights, in cm, of a Yr 10
group of Year 10 students.
Yr 7
130
a) The table shows information about
the heights, in cm, of a group
of Year 7 students.
Complete the boxplot for Year 7.
b) The heights distributions of Year 10
and Year 7 are compared.
140
height
(cm)
150
160
Height (cm)
median
170
least
upper
lower
quartile quartile
height
145 158 154 166
range
25
A- The median height is higher for Yr 7 than for Yr 10
Select the statements that apply. B-The interquartile range is higher for Yr 7 than for Yr 10
C - The data range is wider for Yr 7 than for Yr 10
D- The median height is lower for Yr 7 than for Yr 10
180
(3)
(2)
Total marks: 5

Answer 1

A - The median height is higher for Yr 7 than for Yr 10.

B - The interquartile range is higher for Yr 7 than for Yr 10.

C - The data range is wider for Yr 7 than for Yr 10.

Step-by-step explanation:

The box plot and accompanying data indicate that the median height for Year 7 students is higher than that of Year 10 students. This is supported by the fact that the median value for Year 7 is 158 cm, while for Year 10, it is 154 cm. This aligns with statement A, stating that the median height is higher for Year 7.

Furthermore, the interquartile range (IQR) for Year 7 is wider than that of Year 10. The IQR is a measure of statistical dispersion, and a larger IQR indicates greater variability in the data. In this case, the IQR for Year 7 is 12 cm (166 - 154), whereas for Year 10, it is 10 cm (160 - 150). This supports statement B, stating that the interquartile range is higher for Year 7 than for Year 10.

Lastly, the data range, which represents the spread of the entire dataset, is wider for Year 7 than for Year 10. The data range for Year 7 is 25 cm (from 130 to 155), while for Year 10, it is 10 cm (from 150 to 160). This confirms statement C, stating that the data range is wider for Year 7 than for Year 10.

Answer 2

The box plot shows information

about the heights, in cm, of a Yr 10

group of Year 10 students.

Yr 7

130

a) The table shows information about

the heights, in cm, of a group

of Year 7 students.

Complete the boxplot for Year 7.

b) The heights distributions of Year 10

and Year 7 are compared.

140

height

(cm)

150

160

Height (cm)

median

170

least

upper

lower

quartile quartile

height

145 158 154 166

range

25

A- The median height is higher for Yr 7 than for Yr 10

Select the statements that apply. B-The interquartile range is higher for Yr 7 than for Yr 10

C - The data range is wider for Yr 7 than for Yr 10

D- The median height is lower for Yr 7 than for Yr 10

180

(3)

(2)

Total marks: 5

Step-by-step explanation:

A - The median height is higher for Yr 7 than for Yr 10. (Incorrect)

B - The interquartile range is higher for Yr 7 than for Yr 10. (Correct)

C - The data range is wider for Yr 7 than for Yr 10. (Correct)

D - The median height is lower for Yr 7 than for Yr 10. (Incorrect)

Therefore, the correct statements are B and C.