1. The following table shows the age distribution of teachers who smoke at Laughlin High School.

Ages Number of smokers

20 ≤ x < 30 5

30 ≤ x < 40 4

40 ≤ x < 50 3

50 ≤ x < 60 2

60 ≤ x < 70 3

(a) Calculate an estimate of the mean smoking age.

1

(b) On the following grid, construct a histogram to represent this data.

Working:

Answers:

(a) …………………………………………..

(Total 4 marks)

2

2. The bar chart below shows the number of people in a selection of families.

1 0

8

6

4

2

03 4 5 6 7 8 9 1 0

N u m b e r o f p e o p le in a fa m ily

N u m b er o ffam ilie s

(a) How many families are represented?

(b) Write down the mode of the distribution.

(c) Find, correct to the nearest whole number, the mean number of people in a family.

Working:

Answers:

(a) ..................................................................(b) ..................................................................(c) ..................................................................

(Total 4 marks)

3

3. The number of hours that a professional footballer trains each day in the month of June is represented in the following histogram.

1 0

9

8

7

6

5

4

3

2

1

0 1 2 3 4 5 6 7 8 9 1 0n u m b er o f h o u rs

num

ber o

f day

s

(a) Write down the modal number of hours trained each day.

4

(b) Calculate the mean number of hours he trains each day.

Working:

Answers:

(a) ..................................................................(b) ..................................................................

(Total 8 marks)

4. The histogram below shows the amount of money spent on food each week by 45 families. The amounts have been rounded to the nearest 10 dollars.

1 5 0 1 6 0 1 7 0 1 8 0 1 9 0$

freq

uenc

y

1 81 61 41 21 0

86420

(a) Calculate the mean amount spent on food by the 45 families.

(b) Find the largest possible amount spent on food by a single family in the modal group.

(c) State which of the following amounts could not be the total spent by all families in the modal group:

(i) $2430 (ii) $2495 (iii) $2500 (iv) $2520 (v) $2600

5

A n sw ers:

Work in g:

(a ) ......... .. .. ......... . .. ... .. .. .. .. .. .. ....... .. ....

(b ) ............. .. .. ....... .. .. .. .. .. .. .. .. .. ... .. .. ....

(c ) ... .. .. .. .. .. .. .. ... .. .. .. .. .. .. .................. .. .(Total 6 marks)

5. The heights in cm of the members of 4 volleyball teams A, B, C and D were taken and represented in the frequency histograms given below.

fre q u en cy

1 8 0h e ig h t (c m )

A

1 9 0 2 0 0

fre q u en cy

1 8 0h e ig h t (c m )

C

1 9 0 2 0 0

freq u e n cy

1 8 0h e ig h t (c m )

B

1 9 0 2 0 0

freq u e n cy

1 8 0h e ig h t (c m )

D

1 9 0 2 0 0

6

The mean x and standard deviation of each team are shown in the following table.

I II III IV

x 194 189 188 195

6.50 4.91 3.90 3.74

Match each pair of x and (I, II, III, or IV) to the correct team (A, B, C or D).

x and Team

I

II

III

IV

Workin g :

(Total 6 marks)

7

6. The figure below shows the lengths in centimetres of fish found in the net of a small trawler.

111 0

987654321

– 10 1 0

N u m b er o ffish

2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 11 0 1 2 0 1 3 0

L en g th (cm )

(a) Find the total number of fish in the net.(2)

(b) Find (i) the modal length interval;

(ii) the interval containing the median length;

(iii) an estimate of the mean length.(5)

(c) (i) Write down an estimate for the standard deviation of the lengths.

(ii) How many fish (if any) have length greater than three standard deviations above the mean?

(3)

The fishing company must pay a fine if more than 10 of the catch have lengths less than 40cm.

(d) Do a calculation to decide whether the company is fined.(2)

8

A sample of 15 of the fish was weighed. The weight, W was plotted against length, L as shown below.

1 .2

1

0 .8

0 .6

0 .4

0 .2

W(k g )

0 2 0 4 0 6 0 8 0 1 0 0L (c m )

(e) Exactly two of the following statements about the plot could be correct. Identify the two correct statements.

(2)

Note: You do not need to enter data in a GDC or to calculate r exactly.

(i) The value of r, the correlation coefficient, is approximately 0.871.

(ii) There is an exact linear relation between W and L.

(iii) The line of regression of W on L has equation W = 0.012L + 0.008.

(iv) There is negative correlation between the length and weight.

(v) The value of r, the correlation coefficient, is approximately 0.998.

(vi) The line of regression of W on L has equation W = 63.5L + 16.5.(Total 14 marks)

9

7. A random sample of 167 people who own mobile phones was used to collect data on the amount of time they spent per day using their phones. The results are displayed in the table below.

Time spent perday (t minutes) 0 t 15 15 t

3030 t

4545 t

6060 t

7575 t

90

Number of people 21 32 35 41 27 11

(a) State the modal group.(1)

(b) Use your graphic display calculator to calculate approximate values of the mean and standard deviation of the time spent per day on these mobile phones.

(3)

(c) On graph paper, draw a fully labelled histogram to represent the data.(4)

(Total 8 marks)

10

8. The table below shows the number of words in the extended essays of an IB class.

Number ofwords 3200w3400 3400w3600 3600w3800 3800w4000 4000w4200

Frequency 2 5 8 17 3

(a) Draw a histogram on the grid below for the data in this table.

5

1 0

1 5

2 0

3 0 0 0 3 2 0 0 3 4 0 0 3 6 0 0 3 8 0 0 4 0 0 0 4 2 0 0 4 4 0 0

Freq

uenc

y

N u m b e r o f w o rd s

0

(3)

(b) Write down the modal group.(1)

The maximum word count is 4000 words.

(c) Write down the probability that a student chosen at random is on or over the word count.(2)

Wo rking :

A n sw ers:

(c ) ............ ..... .. .. .. .. ............... .. .. .. .. .. .

(b ) ......... .. . ... .. .. .. .. .. ..... .. .. .. .. .. .. .. .. .. .. .

(Total 6 marks)

11

12

9. The following histogram shows the weights of a number of frozen chickens in a supermarket. The weights are grouped such that 1 weight 2, 2 weight, 3 and so on.

5 5

5 0

4 5

4 0

3 5

3 0

2 5

2 0

1 5

1 0

5

06543210

n u m b e r o fch ick en s

w e ig h t (k g )

(a) On the graph above, draw in the frequency polygon.(2)

(b) Find the total number of chickens.(1)

(c) Write down the modal group.(1)

Gabriel chooses a chicken at random.

(d) Find the probability that this chicken weighs less than 4 kg.(2)

13

A n sw ers:

Work in g:

(a ) ..... .. ......... .. .. ... .. ........... .. .. .. .. ..... . ...

(b ) ..... .. .. .. ......... .. ................ .. .. ........ .. .

(c ) ............. .. .. ......... .. .. .. .. .. .. .. .. ... .. .. ....(Total 6 marks)

10. The following stem and leaf diagram gives the heights in cm of 39 schoolchildren.

Stem Leaf Key 13 2 represents 132 cm.

131415161718

2, 3, 3, 5, 8, 1, 1, 1, 4, 5, 5, 9, 3, 4, 4, 6, 6, 7, 7, 7, 8, 9, 9,1, 2, 2, 5, 6, 6, 7, 8, 8,4, 4, 4, 5, 6, 6,0,

(a) (i) State the lower quartile height.

(ii) State the median height.

(iii) State the upper quartile height.

14

(b) Draw a box-and-whisker plot of the data using the axis below.

1 2 0 1 3 0 1 4 0 1 5 0 1 6 0 1 7 0 1 8 0 1 9 0

h e ig h t in cm

Wo rk in g :

A nsw ers:

(a ) (i) .... .............. .. . .. .. ................

(i i) ........... .. .. .. .. .. .. .. ......... .. .. ..

(i ii) .... .. . ... .. .. .. .. .. ....... .. .. .. .. .. ..

(Total 6 marks)

15

11. The following results give the heights of sunflowers in centimetres.

180 184 195 177 175 173 169 167 197 173 166 183 161 195 177192 161 165

Represent the data by a stem and leaf diagram.(Total 6 marks)

12. The following stem and leaf diagram gives the weights in kg of 34 eight year-old children.

S tem L e af2 6 1 , 22 7 2 , 4 , 42 8 0 , 1 , 6 , 62 9 2 , 2 , 4 , 4 , 53 0 0 , 1 , 2 , t , 6 , 8 , 8 , 93 1 3 , 3 , 5 , 6 , 63 2 1 , 3 , 5 , 5 , 83 3 0 , 4

K ey : 2 6 ° 1 rea d s 2 6 .1k g

(a) The median weight is 30.3 kg. Find the value of t.

(b) Write down the lower quartile weight.

(c) The value of the upper quartile is 31.6 kg and there are no outliers. Draw a box and whisker plot of the data using the axis below.

Weig h t (k g )2 6 2 7 2 8 2 9 3 0 3 1 3 2 3 3 3 4

16

A n sw ers:

Work in g:

(a ) ......... .. .. ......... . .. ... .. .. .. .. .. .. ....... .. ....

(b ) ............. .. .. ....... .. .. .. .. .. .. .. .. .. ... .. .. ....

(c ) ... .. .. .. .. .. .. .. ... .. .. .. .. .. .. .................. .. .(Total 6 marks)

13. The birth weights, in kilograms, of 27 babies are given in the diagram below.

1 7 , 8 , 9 k ey 1 |7 = 1 .7 k g2 1 , 2 , 2 , 3 , 5 , 5 , 7 , 8 , 93 0 , 1 , 3 , 4 , 5 , 5 , 6 , 6 , 7 , 94 1 , 1 , 2 , 3 , 7

(a) Calculate the mean birth weight.(2)

(b) Write down:

(i) the median weight;(1)

(ii) the upper quartile.(1)

The lower quartile is 2.3 kg.

(c) On the scale below draw a box and whisker diagram to represent thebirth weights.

(2)

1 2 3 4 5Weig h t (k g )

17

Wo rk in g :

A nsw ers:

(a ) .... .. .. .... .. .. .. .. .. .. ................ .. .. .. .. .. .

(b ) (i) ............ .. .. .. .. .. ........... .. .. .. .. .. .

(ii) ..... .. .. .. .. .. .. .. .. .. ..... .. .. .. .. ... . .. .(Total 6 marks)

18

14. (a) Complete the following table of values for the height and weight of seven students.

Values Mode Median Mean Standarddeviation

Height (cm) 151, 158, 171, 163, 184, 148, 171 164 11.7

Weight (kg) 53, 61, 58, 82, 45, 72, 82 82 61

(4)

The ages (in months) of seven students are 194, 205, 208, 210, 200, 226, 223.

(b) Represent these values in an ordered stem and leaf diagram.

Wo rking :

(2)(Total 6 marks)

19

15. The table shows the number of children in 50 families.

Number ofchildren

Frequency Cumulativefrequency

1 3 3

2 m 22

3 12 34

4 p q

5 5 48

6 2 50

T

(a) Write down the value of T.

(b) Find the values of m, p and q.

Working:

Answers:(a) …………………………………………..(b) …………………………………………..

(Total 4 marks)

20

16. A marine biologist records as a frequency distribution the lengths (L), measured to the nearest centimetre, of 100 mackerel. The results are given in the table below.

Length of mackerel(L cm)

Number ofmackerel

27 < L ≤ 29 2

29 < L ≤ 31 4

31 < L ≤ 33 8

33 < L ≤ 35 21

35 < L ≤ 37 30

37 < L ≤ 39 18

39 < L ≤ 41 12

41 < L ≤ 43 5

100

(a) Construct a cumulative frequency table for the data in the table.(2)

(b) Draw a cumulative frequency curve.

Hint: Plot your cumulative frequencies at the top of each interval.(3)

(c) Use the cumulative frequency curve to find an estimate, to the nearest cm for

(i) the median length of mackerel;(2)

(ii) the interquartile range of mackerel length.(2)

(Total 9 marks)

21

17. The following table shows the times, to the nearest minute, taken by 100 students to complete a mathematics task.

Time (t) minutes 11–15 16–20 21–25 26–30 31–35 36–40

Number of students 7 13 25 28 20 7

(a) Construct a cumulative frequency table. (Use upper class boundaries 15.5, 20.5 and so on.)

(2)

(b) On graph paper, draw a cumulative frequency graph, using a scale of 2 cm to represent 5 minutes on the horizontal axis and 1 cm to represent 10 students on the vertical axis.

(3)

(c) Use your graph to estimate

(i) the number of students that completed the task in less than 17.5 minutes;

(ii) the time it will take for 43

of the students to complete the task.(2)

(Total 7 marks)

22

18. The graph below shows the cumulative frequency for the yearly incomes of 200 people.

2 0 0

1 8 0

1 6 0

1 4 0

1 2 0

1 0 0

8 0

6 0

4 0

2 0

00 5 0 0 0 1 0 0 0 0 1 5 0 0 0 2 0 0 0 0 2 5 0 0 0 3 0 0 0 0 3 5 0 0 0

A n n u a l in c o m e in B ritish p o u n d s

C u m u la tiv efre q u en cy

23

Use the graph to estimate

(a) the number of people who earn less than 5000 British pounds per year;

(b) the median salary of the group of 200 people;

(c) the lowest income of the richest 20% of this group.

Working:

Answers:

(a) ..................................................................(b) ..................................................................(c) ..................................................................

(Total 4 marks)

24

19. The table below shows the percentage, to the nearest whole number, scored by candidates in an examination.

Marks (%) 0–9 10–19 20–29 30–39 40–49 50–59 60–69 70–79 80–89 90–100

Frequency 2 7 8 13 24 30 6 5 3 2

The following is the cumulative frequency table for the marks.

Marks (%) Cumulative frequency

< 9.5 2

< 19.5 9

< 29.5 s

< 39.5 30

< 49.5 54

< 59.5 84

< 69.5 t

< 79.5 95

< 89.5 98

< 100 100

(a) Calculate the values of s and of t.(2)

25

(b) Using a scale of 1 cm to represent 10 marks on the horizontal axis, and 1 cm to represent 10 candidates on the vertical axis, draw a cumulative frequency graph.

(3)

(c) Use your graph to estimate

(i) the median mark;

(ii) the lower quartile;

(iii) the pass mark, if 40% of the candidates passed.(4)

(Total 9 marks)

26

20. The cumulative frequency graph below shows the examination scores of 80 students.

8 0

7 0

6 0

5 0

4 0

3 0

2 0

1 0

1 0 2 0 3 0 4 0 5 0 6 0sco re s

cu m u la tiv efre q u en c y

0

From the graph find

(a) the median value;

(b) the interquartile range;

(c) the 35th percentile;

27

(d) the percentage of students who scored 50 or above on this examination.

Working:

Answers:

(a) ..................................................................(b) ..................................................................(c) ..................................................................(d) ..................................................................

(Total 8 marks)

21. The heights of 200 students are recorded in the following table.

Height (h) in cm Frequency

140 ≤ h < 150 2

150 ≤ h < 160 28

160 ≤ h < 170 63

170 ≤ h < 180 74

180 ≤ h < 190 20

190 ≤ h < 200 11

200 ≤ h < 210 2

(a) Write down the modal group.(1)

(b) Calculate an estimate of the mean and standard deviation of the heights.(4)

28

The cumulative frequency curve for this data is drawn below.

2 0 0

1 8 0

1 6 0

1 4 0

1 2 0

1 0 0

8 0

6 0

4 0

2 0

01 4 0 1 5 0 1 6 0 1 7 0 1 8 0 1 9 0 2 0 0 2 1 0

h e ig h t in cm

num

ber o

f stu

dent

s

(c) Write down the median height.(1)

(d) The upper quartile is 177.3 cm. Calculate the interquartile range.(2)

(e) Find the percentage of students with heights less than 165 cm.(2)

(Total 10 marks)

29

22. The cumulative frequency table below shows the ages of 200 students at a college.

Age Number of Students Cumulative Frequency

17 3 3

18 72 75

19 62 137

20 31 m

21 12 180

22 9 189

23–25 5 194

> 25 6 n

(a) What are the values of m and n?

(b) How many students are younger than 20?

(c) Find the value in years of the lower quartile.

Working:

Answers:

(a) ..................................................................(b) ..................................................................(c) ..................................................................

(Total 8 marks)

30

23. The table below shows the number and weight (w) of fish delivered to a local fish market one morning.

weight (kg) frequency cumulative frequency

0.50 ≤ w < 0.70 16 16

0.70 ≤ w < 0.90 37 53

0.90 ≤ w < 1.10 44 c

1.10 ≤ w < 1.30 23 120

1.30 ≤ w < 1.50 10 130

(a) (i) Write down the value of c.(1)

(ii) On graph paper, draw the cumulative frequency curve for this data. Use a scale of 1 cm to represent 0.1 kg on the horizontal axis and 1 cm to represent 10 units on the vertical axis. Label the axes clearly.

(4)

(iii) Use the graph to show that the median weight of the fish is 0.95 kg.(1)

(b) (i) The zoo buys all fish whose weights are above the 90th percentile.How many fish does the zoo buy?

(2)

(ii) A pet food company buys all the fish in the lowest quartile. What is the maximum weight of a fish bought by the company?

(3)

(c) A restaurant buys all fish whose weights are within 10% of the median weight.

(i) Calculate the minimum and maximum weights for the fish bought by the restaurant.

(2)

31

(ii) Use your graph to determine how many fish will be bought by the restaurant.(3)

(Total 16 marks)

24. The cumulative frequency graph has been drawn from a frequency table showing the time it takes a number of students to complete a computer game.

2 0 0

1 8 0

1 6 0

1 4 0

1 2 0

1 0 0

8 0

6 0

4 0

2 0

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0 5 5 6 0T im e in m in u te s

Num

ber o

f stu

dent

s

f

(a) From the graph find

(i) the median time;

(ii) the interquartile range.(5)

32

The graph has been drawn from the data given in the table below.

Time in minutes Number of students

0 < x ≤ 5 20

5 < x ≤ 15 20

15 < x ≤ 20 p

20 < x ≤ 25 40

25 < x ≤ 35 60

35 < x ≤ 50 q

50 < x ≤ 60 10

(b) Using the graph, find the values of p and q.(2)

(c) Calculate an estimate of the mean time taken to finish the computer game.(4)

(Total 11 marks)

25. The local council has been monitoring the number of cars parked near a supermarket on an hourly basis. The results are displayed below.

Parked Cars/Hour Frequency Cumulative Frequency

0–19 3 3

20–39 15 18

40–59 25 w

60–79 35 78

80–99 17 95

(a) Write down the value of w.

33

(b) Draw and label the Cumulative Frequency graph for this data.

(c) Determine the median number of cars per hour parked near the supermarket.

Workin g:

A n sw ers:

(a ) ............ .. .. .. ..... .. .. .. .. .. .. .. .. .. .. ... .. ..

(c ) ... .. .. .. .. .. ... .. .. .. ...... ................ ......

(Total 8 marks)

26. There are 120 teachers in a school. Their ages are represented by the cumulative frequency graph below.

34

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0 5 5 6 0 6 5 7 0 7 5A g e

1 3 0

1 2 0

11 0

1 0 0

9 0

8 0

7 0

6 0

5 0

4 0

3 0

2 0

1 0

0

Cum

ulat

ive

freq

uenc

y

(a) Write down the median age.(1)

(b) Find the interquartile range for the ages.(2)

(c) Given that the youngest teacher is 21 years old and the oldest is 72 years old, represent the information on a box and whisker plot using the scale below.

0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0 4 5 5 0 5 5 6 0 6 5 7 0 7 5A g e

(3)

35

Wo rking :

A n sw ers:

(a ) ........... ..... .. .. .. .. .. .. .. .. .. ...............

(b ) .... .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. ... . .. .. ......(Total 6 marks)

36

27. A random sample of 200 females measured the length of their hair in cm. The results are displayed in the cumulative frequency curve below.

2 0 0

1 7 5

1 5 0

1 2 5

1 0 0

7 5

5 0

2 5

05 04 54 03 53 02 52 01 51 050

Cum

ulat

ive

freq

uenc

y

le n g th (cm )

(a) Write down the median length of hair in the sample.(1)

(b) Find the interquartile range for the length of hair in the sample.(2)

(c) Given that the shortest length was 6 cm and the longest 47 cm, draw and label a box and whisker plot for the data on the grid provided below.

5 04 54 03 53 02 52 01 51 050len g th (cm )

(3)

37

Wo rking :

A n sw ers:

(a ) ........... ..... .. .. .. .. .. .. .. .. .. ...............

(b ) .... .. .. .. .. .. .. .. .. .. ... .. .. .. .. .. ... . .. .. ......(Total 6 marks)

38

28. (a) The exam results for 100 boys are displayed in the following diagram:

0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0

(i) Find the range of the results.

(ii) Find the interquartile range.

(iii) Write down the median.

39

(b) The exam results for 100 girls are displayed in the diagram below:

1 0 0

9 0

8 0

7 0

6 0

5 0

4 0

3 0

2 0

1 0

01 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0

ex am re su lts

num

ber o

f girl

s cum

ulat

ive

freq

uenc

y

(i) Write down the median.

(ii) Find the inter quartile range.

(c) Write down the set of results that are the most spread out and give a reason for your answer.

(Total 6 marks)

40

29. The heights (cm) of seedlings in a sample are shown below.

6 3 , 7 k ey 6 3 rep re sen ts 6 3 c m7 2 , 5 , 88 3 , 6 , 6 , 8 , 89 2 , 5 , 7 , 8

1 0 3 , 6 , 611 2 , 2

(a) State how many seedlings are in the sample.

(b) Write down the values of

(i) the median;

(ii) the first and third quartile.

(c) Calculate the range.

(d) Using the scale below, draw a box and whisker plot for this data.

6 0 7 0 8 0 9 0 1 0 0 11 0 1 2 0

41

Wo rkin g :

A nsw ers:

(a ) ..... ... .. . ..... .. .... .. .. .... .. ... .. .. ...... .. .... .

(b ) (i) .... .. .. .. .. .. .. .. .... ... .. .. .. .. .. .. .. ... . .

(i i) ...... .. .... .. .... ... . .. .. ... . ... .. .... .. .. .

(c ) ... .. ... .. . ..... .. .... .. .. .... .. ... .. .. ...... .. .... .(Total 6 marks)

30. (a) State which of the following sets of data are discrete.

(i) Speeds of cars travelling along a road.

(ii) Numbers of members in families.

(iii) Maximum daily temperatures.

(iv) Heights of people in a class measured to the nearest cm.

(v) Daily intake of protein by members of a sporting team.

42

The boxplot below shows the statistics for a set of data.

2 4 6 8 1 0 1 2 1 4 1 6 1 8 2 0d a ta v a lu e s

(b) For this data set write down the value of

(i) the median;

(ii) the upper quartile;

(iii) the minimum value present.

(c) Write down three different integers whose mean is 10.

A n sw ers:

Work in g:

(a ) ....................... .. ..... .. .. .. .. .. .. .. ... ..(b )

(c ) ....................... .. ..... .. .. .. .. .. .. .. ... ..

(i) ..... .............. .. .. .. .. .. .. .. .. ... ..

(ii)..... ....... .. .. .. .. .. .. .. ... .. . .......

(ii i) .... .. .. .. .. ... .. .. .. .. .. ....... ......

(Total 6 marks)

43