QUESTION 1 (20 Marks)

State whether each of the statements below is TRUE or FALSE. If FALSE, provide a reason.

1.1. In a data set, the range is a measure of dispersion.

1.2. The most frequently occurring value in a data set is called the median.

1.3. The most passive data collection method is observation.

1.4. In linear correlation, a Pearson's correlation coefficient of 0.9 indicates a strong and direct relationship between the

variables.

1.5. The result of a PSL soccer match is an example of a binomial experiment.

1.6. Approximately 82% of the area below the normal distribution curve lies between =1.20 and =+1.50.

1.7. The volume of water consumed by an athlete during the Comrades Marathon is quantitative and discrete.

1.8. In a data set, 3>2>1.

QUESTION 2 (20 Marks)

The following data give the hourly wage rates (Rands) for a sample of 20 workers selected from a large company.

12.50 9.45 13.85 7.25 8.70 14.60 11.75 14.50 10.80 12.45

7.50 15.90 9.75 11.50 13.30 6.25 15.50 12.80 5.35 9.50

2.1. Using the raw data, determine the range. (2 marks)

2.2. Fill in the missing values in the table below. (12 marks)

Interval

(Rand)

Frequency

Cumulative

Frequency

5.00 < 7.00

7.00 < 9.00

9.00 < 11.00

11.00 < 13.00

13.00 < 15.00

15.00 < 17.00

20

2.3. Determine the mean wage rate using the raw data. (2 marks)

2.4. Find the median. (2 marks)

2.5. Is there a mode? Explain. (2 marks)

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QUESTION 3 (20 Marks)

The following data represents the volume (in kilolitres) of water used by 30 South African families on a particular day.

Volume (kL)

Frequency

20 < 35

4

35 < 50

10

50 < 65

7

65 < 80

5

80 < 95

4

3.1. Fill in the table below. (10 marks)

3.2. Hence, determine the:

3.2.1. mean. (4 marks)

3.2.2. standard deviation. (6 marks)

QUESTION 4 (20 Marks)

4.1. Medical research has shown that 25% of people are gluten-intolerant. Consider a randomly chosen sample of eight

people. Let the successful outcome be that a person is gluten-intolerant.

4.1.1. Write down each of the following values

(i) (1 marks)

(ii) (1 marks)

4.1.2. What is the probability that exactly 4 are people in this sample is gluten-intolerant. (4 marks)

4.1.3. at most 1 person is gluten-intolerant. (6 marks)

4.2. State two properties of the normal distribution function. (2 marks)

Volume (kL)

Frequency

f

Midpoint

m

fm

fm2

20 < 35

4

27.5

35 < 50

10

42.5

50 < 65

7

57.5

65 < 80

5

72.5

80 < 95

4

87.5

30

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4.3. It is known that 20.61% of students in a Mathematics class got a higher mark than Eric. The marks are normally distributed with a mean of 56 points and a standard deviation of 8 points. 4.3.1. What is the value of ? (2 marks) 4.3.2. Calculate Eric's mark, to the nearest integer. (4 marks)

QUESTION 5

(20 Marks)

A nutritionist suggests that eating avocadoes frequently improves cardiovascular health. The table below shows the cholesterol levels (in mmol/L) of 5 males as well as the number of avocadoes they consumed per week.

Number of avocadoes consumed per week

Cholesterol reading (mmol/L)

1

6.0

2

5.5

3

5.2

4

4.4

5

4.0

5.1. Fill in the missing values in the table below. (6 marks)

5.2. Hence, calculate Pearson's correlation coefficient. (4 marks)

5.3. The linear regression equation has the form =+. Determine the value of:

5.3.1. (4 marks)

5.3.2. (3 marks)

5.4. Use the equation to predict the number of avocadoes consumed per week by a

male who has a cholesterol reading of 3.5. (3 marks)

x

y

xy

x2

y2

1

6.0

6.0

1

36.0

2

5.5

P

4

30.25

3

5.2

15.6

Q

27.04

4

4.4

17.6

16

S

5

4.0

20.0

25

16.0

15

T

U

V

128.65

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QUESTION 6 (20 Marks)

Name and elaborate on the components of a time series.