Statistics

Standard Grade – Final Revision

The table shows the number of children in a family for a survey carried out in a large village. Construct a cumulative frequency column

for this table and use it to determine the median and the semi- interquartile range.

Number ofchildren

Number offamilies

0 38

1 56

2 74

3 31

4 24

5 9

The table shows the favourite holiday destinations for a group of people. It is intended to use this information to produce a pie-chart.

What angle in the pie chart will be used to represent each country chosen?

Country Number of people

Italy 13

U.S.A. 28

France 15

Australia 9

Canada 28

Germany 27

The table shows the mode of transport to school for a number of pupils.

If a pupil is chosen at random calculatep (Pupil comes to school by bus)

p (Girl who walks)p (Pupil does not come by car)

Car Bus Walk Train

Boys 34 43 55 12

Girls 56 40 65 8

Tests are to be carried out on a new type of chicken food to see if the new food significantly increases the weight of the chickens. Fifteen chickens are given the new food and another fifteen are

fed on the usual chicken food. The weight increases in the chickens are recorded over a short period of time and these results

are shown in the tables below. Draw a back to back stem and leaf diagram to compare the figures.

Weight increase ( in Kg) – usual food Weight increase ( in Kg) – new food

3.6 5.6 4.8 2.2 2.5

1.6 3.6 4.3 4.2 3.1

3.4 3.3 3.0 4.9 6.3

1.5 0.9 3.1 3.1 3.4

2.8 1.4 2.5 2.9 1.8

1.9 1.6 3.3 2.3 3.0

The strength of cables was measured in an experiment by testing 10 different cables

to breaking point by hanging heavy loads (tons) at the centre of the cable.

The following results were obtained ∑ loads = 35.9 ∑ loads2 = 147.03

Calculate the mean and standard deviation of the breaking strength of the cables giving

your answers correct to 1 decimal place.

The rainfall over a certain period was observed and the results are given in the diagram above.

Calculate the average rainfall over the period

A firm employs 32 workers under the age of 18 years and 45 workers over the age of 18 years.

The average wage of those less than 18 years is ₤268 per week while the

average age of those over 18 years is ₤282 per week. Find the average wage for the whole work force.

Two dice are thrown. Calculate a) p (sum of the two dice is 9)

b) p (sum of two dice is less than 4)

Consider the numbers 2,3,5,8,11,17,20,21,25,30,48,60One of the numbers is selected at random. Calculate

a) p (multiple of 5) b) p (factor of 60)

c) p (prime)

The figures below show the total length, in mm, of starlings captured

during a bird ringing exercise. 184 193 189 214 198 208

Calculate the mean and standard deviation for these measurements giving your answers correct to 1 decimal place.

14

3

25

Bag A

3 4

Bag B

5

There are two bags A and B. Bag A contains the numbered balls 1, 2, 3, 4 and 5.

Bag B contains the balls numbered 3, 4, and 5 as shown in the diagram.

A ball is drawn at random from each bag.List all the possible outcomes.

Calculate a) The probability that the sum of the two balls is odd.

b) The probability that the sum of the two balls is 6.

Marks in Exams

Physics mark

10

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20

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60

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70

80

80

90

90

100

100

Mat

hs M

ark

10

10

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30

30

40

40

50

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60

60

70

70

80

80

90

90

100

100

The diagram shows pupils marks in Physics and Maths exams. On the diagram draw what in your opinion is the best fitting

straight line through the points. Choose two points on this line and find the equation

of the line. Use this equation to estimate the Maths mark for a pupil who scored 72% in the

Physics exam but missed the Maths exam.

A class survey showed the number of pupils involved in different sports to

be as follows. Draw an appropriate statistical

diagram to illustrate this information.

Sport Numberof pupils

Hockey 7

Football 2

Rugby 11

Cricket 3

Athletics 7

A survey was carried out to see how many bookswere being carried by pupils in their schoolbags. The results are shown in the bar chart opposite.

Make up a frequency table and find the mean.Add in a cumulative frequency column and use

it to determine the median number of books being carried by pupils

The table shows the number of pupils entering the Math's competitions held in the school.

If a pupil is selected at random from those entering the competitions calculate

P (Girl entering a competition)P (Pupil entering the Intermediate competition)

P (Boy entering the Junior competition)

Boys Girls

Junior 34 26

Intermediate 28 25

Senior 14 6