[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: 8]

Each year the total number of hours, x, of sunshine in Kintoo is recorded during the month of June. The results for the last 60 years are summarised in the table.

(a)

Draw a cumulative frequency graph to illustrate the data.

[ 3 ]

(b)

Use your graph to estimate the 70th percentile of the data.

[ 2 ]

(c)

Calculate an estimate for the mean number of hours of sunshine in Kintoo during June over the last 60 years.

[ 3 ]

[Maximum number: 3]

50 values of the variable x are summarised by

\Sigma(x-20)=35 \quad \text { and } \quad \Sigma x^{2}=25036 .

Find the variance of these 50 values.

[Maximum number: 4]

A summary of 50 values of x gives

\Sigma(x-q)=700, \quad \Sigma(x-q)^{2}=14235

where q is a constant.

(a)

Find the standard deviation of these values of x.

[ 2 ]

(b)

Given that $\Sigma x=2865$ , find the value of q.

[ 2 ]

[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: 4]

The times taken by 120 children to complete a particular puzzle are represented in the cumulative frequency graph.

(a)

Use the graph to estimate the interquartile range of the data.

[ 2 ]

(b)

35\% of the children took longer than T seconds to complete the puzzle.

Use the graph to estimate the value of T.

[ 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: 4]

A summary of 20 values of x gives

\sum(x-30)=439, \quad \sum(x-30)^{2}=12405 .

A summary of another 25 values of x gives

\sum(x-30)=470, \quad \sum(x-30)^{2}=11346 .

(a)

Find the mean of all 45 values of x.

[ 2 ]

(b)

Find the standard deviation of all 45 values of x.

[ 2 ]

[Maximum number: 7]

The times, t minutes, taken to complete a walking challenge by 250 members of a club are summarised in the table.

(a)

Draw a cumulative frequency graph to illustrate the data.

[ 2 ]

(b)

Use your graph to estimate the 60th percentile of the data.

[ 1 ]

(c)

It is given that an estimate for the mean time taken to complete the challenge by these 250 members is 34.4 minutes.

Calculate an estimate for the standard deviation of the times taken to complete the challenge by these 250 members.

[ 4 ]

Question 1

Question 1(a)

Question 1(b)

Question 1

Question 1(a)

Question 1(b)

Question 1(c)

Question 1

Question 1

Question 1(a)

Question 1(b)

Question 1

Question 1

Question 1(a)

Question 1(b)

Question 1(c)

Question 1

Question 1(a)

Question 1(b)

Question 1

Question 1(a)

Question 1(b)

Question 1

Question 1(a)

Question 1(b)

Question 3

Question 3(a)

Question 3(b)

Question 3(c)