Year 7 Statistics Pretest

Name:

Date:

Part 1: Data and Summary Statistics

Answer each question. Show your working where needed.

1. Classify each variable as discrete numerical, continuous numerical or not numerical.

a) The number of books students read this month: __________

b) The height of each student in centimetres: __________

c) The colour of each student’s school bag: __________

d) The temperature at lunchtime in °C: __________

2. A teacher wants to find out how students travel to school. Write one suitable primary source and one suitable secondary source of data.

Primary source: ____________________________________________________

Secondary source: __________________________________________________

3. The numbers of goals scored by a team in seven matches were:

3, 5, 5, 6, 7, 8, 8

Find the:

a) range: __________ b) median: __________ c) mean: __________

d) mode or modes: ____________________

4. Consider the data set: 4, 5, 5, 6, 6, 7, 8, 30.

a) Identify the outlier: __________

b) Find the median: __________

c) Find the mean, correct to one decimal place: __________

d) Which is more useful for describing the typical value, the mean or median? Explain why.

5. Two classes recorded the number of minutes they spent reading last night.

Class A: 10, 10, 15, 15, 15, 20, 20, 25

Class B: 5, 10, 15, 20, 20, 25, 30, 35

a) Find the median for each class.

b) Which class has the greater range?

c) Which class appears more spread out? Give one reason.

6. A news report says, “The average house price in a suburb is $1,200,000.” Most houses cost between $500,000 and $700,000, but two very expensive houses cost more than $5,000,000.

Which measure is probably being reported: mean or median? Explain why the report could be misleading.

Part 2: Representing and Interpreting Distributions

7. The numbers of pets owned by nine students are:

1, 2, 2, 3, 3, 3, 4, 5, 5

Construct a dot plot. Then state the mode, median and range.

Mode: __________ Median: __________ Range: __________

8. The following data show the times, in minutes, taken by students to complete a puzzle:

12, 14, 15, 18, 21, 21, 23, 27, 30

a) Complete a stem-and-leaf plot using the tens digit as the stem.

b) Include a key.

c) Find the median and range.

9. A data set has a long tail towards larger values. It has a mean of 18, a median of 14 and a mode of 12.

a) Is the distribution likely to be skewed left or skewed right? __________

b) Which measure of centre would usually be most suitable: mean, median or mode? __________

c) Describe the shape and explain your choice.

10. Compare these two distributions of test scores.

Group A: mean 72, median 73, range 18

Group B: mean 72, median 65, range 40

Write two statements comparing their centre and spread. Suggest which group may contain an outlier.

11. A dot plot has most values between 6 and 10, with one value at 25.

a) What feature of the distribution is 25? __________

b) What should you check before deciding whether it is an error?

c) Explain how this value could affect the mean and range.

Part 3: Statistical Investigation

12. Plan an investigation into the question: “How much time do Year 7 students spend using a screen after school?”

a) Write a clear statistical question.

b) Identify the numerical variable and state whether it is discrete or continuous.

c) Describe how you would collect a fair sample using a primary source.

d) Name one possible source of bias.

e) Choose two suitable displays or summary statistics for reporting the data.

Teacher Answer Key and Marking Guidance

1. a) Discrete numerical. b) Continuous numerical. c) Not numerical. d) Continuous numerical. Award 1 mark each.

2. Accept suitable examples. Primary: survey or ask students directly. Secondary: school attendance records, a published transport report or government data. Award 1 mark for each appropriate source.

3. Range = 8 − 3 = 5; median = 6; mean = 42 ÷ 7 = 6; modes = 5 and 8. Award 1 mark for each correct measure.

4. a) 30. b) Median = (6 + 6) ÷ 2 = 6. c) Mean = 71 ÷ 8 = 8.9, correct to one decimal place. d) Median is more useful because the outlier makes the mean unusually large. Award up to 5 marks.

5. a) Class A median = (15 + 15) ÷ 2 = 15; Class B median = (20 + 20) ÷ 2 = 20. b) Class B has the greater range: 35 − 5 = 30, compared with Class A: 25 − 10 = 15. c) Class B is more spread out because its range is larger. Award up to 4 marks.

6. Probably the mean. The two very expensive houses pull the mean upwards, so it does not represent the typical house price well. The median would be more representative. Award 2 marks.

7. Dot plot should show: 1 appears once, 2 twice, 3 three times, 4 once and 5 twice. Mode = 3; median = 3; range = 5 − 1 = 4. Award 1 mark for the plot and 1 mark for each summary.

8. Stem-and-leaf plot:

1 | 2 4 5 8

2 | 1 1 3 7

3 | 0

Key: 1 | 2 means 12 minutes. Median = 21; range = 30 − 12 = 18. Award up to 5 marks.

9. a) Skewed right. b) Median. c) The long tail is towards larger values; the mean is greater than the median and is pulled upwards by large values. Award 1 mark for each part.

10. Both groups have the same mean, so their mean centre is 72. Group A has a median closer to its mean and a smaller range, so it is less spread out. Group B has greater spread and may contain an outlier, particularly a very high or low score. Award up to 4 marks for valid comparisons.

11. a) 25 is an outlier. b) Check the original recording, measurement and units, and whether the value is genuine. c) It will usually increase the mean and increase the range. Award 1 mark for each part.

12. Award up to 8 marks: clear question (1); variable identified as time and continuous (2); fair primary data collection method (2); possible bias (1); two suitable displays or summaries, such as a dot plot, histogram, stem-and-leaf plot, median, mean or range (2). Strong responses mention a representative sample, consistent units and anonymous responses.

Skills-to-question mapping: Q1: VC2M7ST01; Q2: VC2M7ST01 and VC2M7ST03; Q3–Q6: VC2M7ST01; Q7–Q11: VC2M7ST02; Q12: VC2M7ST03, with links to VC2M7ST01 and VC2M7ST02.