Statistical Diagrams Team Challenge Version A

Team

Statistical Diagrams Team Challenge Version A

1.The incomplete table and histogram give some information about the ages of the people who live in a village.

(a)Use the information in the histogram to complete the frequency table below. (2)

Age (x) in years / Frequency
0 < x 10 / 160
10 < x25
25 < x 30
30 < x 40 / 60
40 < x 70 / 90

(b)Complete the histogram.(2)

(2)

(Total 6 marks)

2.The box plot gives information about the distribution of the weights of bags on a plane.

(a)Jean says the heaviest bag weighs 23 kg. Is she correct? Explain why.

...... (1)

(b)Write down the median weight...... kg(1)

(c)Work out the interquartile range of the weights.

...... kg(1)

(d) There are 240 bags on the plane.Work out the number of bags with a weight of 10 kg or less.

...... (2)

(e) John and Peter each own a garage.They both sell used cars.The box plots show some information about the prices of cars at their garages.

Compare the distribution of the prices of cars in these two garages.
Give two comparisons.

1......

......

2 ......

...... (2)

(Total 7 marks)

3.The table shows information about the ages of 240 members of a sports club.

Age (t years) / Frequency / Cumulative frequency
15 t < 20 / 95
20 t < 25 / 90
25 t < 30 / 35
30 t < 35 / 15
35 t < 40 / 5

A pie chart is to be drawn for the information in the table.

(a)Work out the size of the angle for people in the class 20 t < 25

...... º(2)

(b)Write down the modal class.

...... (1)

(c)Complete the cumulative frequency table. (1)

(d)On the grid, draw the cumulative frequency graph for your table.(2)

(e)Use your graph to find an estimate for the median age of the people.

...... years(2)

(Total 8 marks)

4.Peter is an artist. The scatter graph, right, gives information about the area and the cost of some of his pictures. The line of best fit has been drawn on the graph.

Let x = area

and y = cost

a) Describe the correlation shown in the scatter diagram (1) …………………………………………

b) What does this tell you about the relationship ………………………………………………………

between the cost of the picture and its area. (1) ……………………………………………………..

……………………………………………………..

c) Calculate the gradient of your line of …………………………………………………………

best fit. Explain your answer fully…..(3) ………………………………………………………..

……………………………………………………….

d) hence, write down the equation of the line of best fit (2) y =…………………………..

e) Use your equation to calculate an estimate for the cost of a picture of area 1000 cm2

£…………………………………(2)

f) Use your equation to find an estimate of thearea of a picture costing £800.

…………………………………cm2 (2)

(Total 11 marks)

5.An estate agent has one house for sale for £100 000 and one at £150 000. The diagram has been drawn to represent this information.

(a)Explain why the diagram is misleading in representing these house prices.

......

...... (1)

(b)The agent decides to represent the houses using a two dimensional diagram. The area representing the £100 000 house is 5 cm2.
Calculate the area representing the£150 000 house.

Answer ...... cm2(2)

Imagine a pie chart showing the number of people attending a sell outleague football match at Bloomfield Road.The total number of people attending the match was 15 000. The angle for the sector representing women at the game is 78 degrees.

Answer ...... (3)

The radius of the pie chart 4 cm. A comparative pie chart is to be drawn for an international football match at Wembley which had an attendance of 93 750.

(d) Calculate the radius of the pie chart for the international football match.

Answer ……...... (4)

( Total 10 marks )

6. The table shows the cost of the gas at the end of every three months and some four-point moving averages.

Year / 2002 / 2003 / 2004
Quarter / 1st / 2nd / 3rd / 4th / 1st / 2nd / 3rd / 4th / 1st / 2nd / 3rd / 4th
Cost (£) / 86 / 90 / 93 / 99 / 94 / 94 / 97 / 103 / 94 / 98 / 101
Four-point moving average / 92 / 94 / 95 / 96 / 97 / 97

The graph shows the actual cost of the gas and some of the moving averages.

(a)Calculate the last two four-point moving averages and on the graph plot them.

(4)

(b) Use the trend of the moving averages to predict the cost of the gas used at the end of the 4th quarter of 2004.

( hint:- take a careful lok at the other two 4th quarter gas costs )

………...…...... ……...... …………….....…………......

Answer £ …………………………………

(4)

(Total 8 marks)

7.As part of their job, taxi drivers record the number of miles they travel each day. A random sample of the mileages recorded by taxi drivers Keith and Brian are given in the back-to-back stem and leaf diagram below.

Keith / Brian
8 / 7 / 7 / 4 / 3 / 2 / 1 / 1 / 0 / 18 / 4 / 4 / 5 / 7
9 / 9 / 8 / 7 / 6 / 5 / 4 / 3 / 3 / 1 / 1 / 19 / 5 / 7 / 8 / 9 / 9
8 / 7 / 4 / 2 / 2 / 0 / 20 / 0 / 2 / 2 / 4 / 4 / 8
9 / 4 / 3 / 1 / 0 / 0 / 21 / 2 / 3 / 5 / 6 / 6 / 7 / 9
6 / 4 / 1 / 1 / 22 / 1 / 1 / 2 / 4 / 5 / 5 / 8
2 / 0 / 23 / 1 / 1 / 3 / 4 / 6 / 6 / 7 / 8
7 / 1 / 24 / 2 / 4 / 8 / 8 / 9 / 9
9 / 25
9 / 3 / 26

Key: 0 18 4 means 180 for Keith and 184 for Brian

Keith / Brian
Lower quartile / 191 / a
Median / b / 219
Upper quartile / 221 / c

The quartiles for these two distributions are summarised in the table right.

(a)Find the values of a, b and c.

a =...... b = ...... c = ...... (3)

(b) Find the interquartile ranges for each set of data

Keith’s IQR = ………. Brian’s IQR = …………(2)

Outliers are values that lie outside the limits

Lower Quartile – 1.5xIQR and Upper Quartile + 1.5xIQR

(Total 9 marks)