[Maximum number: 5]

The following back-to-back stem-and-leaf diagram shows the annual salaries of a group of 39 females and 39 males.

Key: 2 | 20 | 3 means $20200for females and $20300 for males.

(a)

Find the median and the quartiles of the females' salaries.

You are given that the median salary of the males is $ 24000, the lower quartile is $ 22600 and the upper quartile is $ 25300.

[ 2 ]

(b)

Draw a pair of box-and-whisker plots in a single diagram on the grid below to represent the data.

[ 3 ]

[Maximum number: 3]

For n values of the variable x, it is given that

\Sigma(x-50)=144 \quad \text { and } \quad \Sigma x=944 .

Find the value of n.

[Maximum number: 5]

The heights in cm of 160 sunflower plants were measured. The results are summarised on the following cumulative frequency curve.

(a)

Use the graph to estimate the number of plants with heights less than 100 cm .

[ 1 ]

(b)

Use the graph to estimate the 65th percentile of the distribution.

[ 2 ]

(c)

Use the graph to estimate the interquartile range of the heights of these plants.

[ 2 ]

[Maximum number: 3]

The time taken, t minutes, to complete a puzzle was recorded for each of 150 students. These times are summarised in the table.

(a)

Draw a cumulative frequency graph to illustrate the data.

[ 2 ]

(b)

Use your graph to estimate the 20th percentile of the data.

[ 1 ]

[Maximum number: 3]

Twenty children were asked to estimate the height of a particular tree. Their estimates, in metres, were as follows.

(a)

Find the mean of the estimated heights.

[ 1 ]

(b)

Find the median of the estimated heights.

[ 1 ]

(c)

Give a reason why the median is likely to be more suitable than the mean as a measure of the central tendency for this information.

[ 1 ]

[Maximum number: 4]

A summary of the speeds, x kilometres per hour, of 22 cars passing a certain point gave the following information:

\Sigma(x-50)=81.4 \text { and } \Sigma(x-50)^{2}=671.0 .

Find the variance of the speeds and hence find the value of $\Sigma x^{2}$ .

[Maximum number: 4]

A summary of 40 values of x gives the following information:

\Sigma(x-k)=520, \quad \Sigma(x-k)^{2}=9640,

where k is a constant.

(a)

Given that the mean of these 40 values of x is 34 , find the value of k.

[ 2 ]

(b)

Find the variance of these 40 values of x.

[ 2 ]

[Maximum number: 7]

The back-to-back stem-and-leaf diagram shows the diameters, in cm, of 19 cylindrical pipes produced by each of two companies, A and B.

Key: 1|35| 3 means the pipe diameter from company A is 0.351 cm and from company B is 0.353 cm .

(a)

Find the median and interquartile range of the pipes produced by company A.

[ 3 ]

(b)

It is given that for the pipes produced by company B the lower quartile, median and upper quartile are $0.346 \mathrm{~cm}, 0.352 \mathrm{~cm}$ and 0.370 cm respectively.

Draw box-and-whisker plots for companies A and B on the grid below.

[ 3 ]

(c)

Make one comparison between the diameters of the pipes produced by companies A and B.

[ 1 ]

[Maximum number: 5]

A sports club has a volleyball team and a hockey team. The heights of the 6 members of the volleyball team are summarised by $\Sigma x=1050$ and $\Sigma x^{2}=193700$ , where x is the height of a member in cm . The heights of the 11 members of the hockey team are summarised by $\Sigma y=1991$ and $\Sigma y^{2}=366400$ , where y is the height of a member in cm .

(a)

Find the mean height of all 17 members of the club.

[ 2 ]

(b)

Find the standard deviation of the heights of all 17 members of the club.

[ 3 ]

[Maximum number: 8]

Two machines, A and B, produce metal rods of a certain type. The lengths, in metres, of 19 rods produced by machine A and 19 rods produced by machine B are shown in the following back-to-back stem-and-leaf diagram.

Key: 7 | 22 | 4 means 0.227 m for machine A and 0.224 m for machine B.

(a)

Find the median and the interquartile range for machine A.

[ 3 ]

(b)

It is given that for machine B the median is 0.232 m , the lower quartile is 0.224 m and the upper quartile is 0.243 m .

Draw box-and-whisker plots for A and B.

[ 3 ]

(c)

Hence make two comparisons between the lengths of the rods produced by machine A and those produced by machine B.

[ 2 ]