# Arithmetic Mean and Marks

Mathematics Department

IB Math Standard-1

Ms. Fabiola Medrano

Name: ______________

Date: May 2, 2013

Total marks: 50 marks

Marks obtained: _____

Score: ______

Quiz 4.2

(Descriptive Statistics II)

General Instructions: Answer each of the following questions on the space provided. You must show ALL your work and IN PEN to earn full credit.

1.

The following table gives the examination grades for 120 students. Grade

Cumulative frequency

1

9

9

2

25

34

3

35

p

4

q

109

5

(a)

Number of students

11

120

Find the value of

(i)

p;

(ii)

q.

(4)

(b)

Find the mean grade.

(2)

(c)

Write down the standard deviation.

(1)

(Total 7 marks)

1

2.

A standard die is rolled 36 times. The results are shown in the following table. Score

2

3

4

5

6

Frequency

(a)

1

3

5

4

6

10

8

Write down the standard deviation.

(2)

(b)

Write down the median score.

(1)

(c)

Find the interquartile range.

(3)

(Total 6 marks)

3.

Consider the four numbers a, b, c, d with a b c ≤ d, where a, b, c, d The mean of the four numbers is 4.

.

The mode is 3.

The median is 3.

The range is 6.

Find the value of a, of b, of c and of d.

(Total 6 marks)

2

The following is the cumulative frequency curve for the time, t minutes, spent by 150 people in a store on a particular day.

150

140

130

120

110

100

cumulative frequency

4.

90

80

70

60

50

40

30

20

10

0

1

2

3

4

5

6

7

8

9

10

11

12

time (t)

(a)

(i)

How many people spent less than 5 minutes in the store?

(ii)

Find the number of people who spent between 5 and 7 minutes in the store.

(iii)

Find the median time spent in the store.

(6)

(Question continues on next page)

3

(b)

Given that 40 of the people spent longer than k minutes, find the value of k. (3)

(c)

(i)

Complete the following frequency table.

t (minutes)

0t2

2t4

Frequency

10

23

(ii)

4t6

6t8

8 t 10

10 t 12

15

Hence, calculate an estimate for the mean time spent in the store. (5)

(Total 14 marks)

5.

A sample of 300 bottles of soft drink was taken from a production line and the contents of each bottle measured for net volume. The sample mean was 377 mL with standard deviation 1.5 mL. (a) Represent this information on a bell-shaped curve.

(3 marks)

(b) How many bottles in the sample would you expect to have contents i.

Between 374 and 380 mL

(2 marks)

ii.

More than 375.5 mL

(2 marks)

(c) What proportion of bottles in the production line would you expect to have contents less than 375.5 mL? (2 marks)

(Total 9 marks)

4

6.

The mean height of players in a basketball competition is 181 cm. If the standard deviation is 4 cm, what percentage of them are likely to be:

(a) Taller than 189 cm

(2 marks)

(b) Taller than 177 cm

(2 marks)

(c) Between 169 cm and 189 cm

(2 marks)

(d) Shorter than 185 cm

(2 marks)

(Total 8 marks)

5

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