Instructions

• Read each question carefully

• Show working for calculation questions

• Circle the correct answer for multiple choice questions

• Time allowed: 45 minutes

📊 Part A: Multiple Choice Questions (10 marks)

1. The data set is: 12, 15, 18, 12, 20, 16, 12. What is the mode?

a) 15

b) 12

c) 16

d) 20

2. For the data set: 8, 12, 15, 20, 25, what is the median?

a) 12

b) 15

c) 16

d) 20

3. The range of a data set is found by:

a) Adding the highest and lowest values

b) Subtracting the lowest from the highest value

c) Finding the middle value

d) Finding the most frequent value

4. If a data set has values: 10, 15, 20, 25, 30, what is the mean?

a) 15

b) 20

c) 25

d) 30

5. Which measure of central tendency is most affected by outliers?

a) Mode

b) Median

c) Mean

d) Range

6. A data set has the following values: 5, 7, 8, 12, 15, 20, 25. What is the interquartile range (IQR)?

a) 10

b) 12

c) 15

d) 20

✏️ Part B: Calculation Questions (10 marks)

7. The test scores for a class are: 65, 72, 78, 65, 84, 90, 76, 65, 88, 70

Calculate the mean score. Show your working.

8. Using the same data from Question 7, find the median score.

Show your working including ordering the data.

9. A basketball team's scores over 8 games were: 85, 92, 78, 85, 96, 88, 85, 91

a) What is the mode? ________________

b) What is the range? Show working: ________________

10. The heights of students in centimetres are: 165, 170, 158, 172, 168, 175, 162

Calculate the mean height to 1 decimal place.

11. Explain why the median might be a better measure of central tendency than the mean when there are extreme outliers in a data set.

12. A survey of 50 students found that their average study time per week is 10 hours with a standard deviation of 2 hours. If a new student studies for 20 hours a week, how does this affect the mean study time of the group? Explain your reasoning.

📝 Answer Key

Part A - Multiple Choice:

1. b) 12 2. b) 15 3. b) Subtracting the lowest from the highest value

4. b) 20 5. c) Mean 6. a) 10

Part B - Calculations:

7. Mean = 753 ÷ 10 = 75.3

8. Ordered: 65, 65, 65, 70, 72, 76, 78, 84, 88, 90. Median = (72 + 76) ÷ 2 = 74

9. a) Mode = 85 b) Range = 96 - 78 = 18

10. Mean = 1170 ÷ 7 = 167.1 cm

11. The median is not affected by extreme values, so it better represents the typical value when outliers are present.

12. The new student's study time would increase the mean study time, as it is significantly higher than the current average. This would indicate that the average study time of the group is now skewed by this outlier.