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Measures of Central Tendency — Free MYP4 Mathematics (Extended) Practice Questions
1QuestionCalculating Mean Median and ModeConcept Practice
2 marks~3 minCriterion A
A school counsellor records the number of siblings for each student in an 11-person advisory group to understand family structures when planning support sessions.
Number of siblings: 0, 0, 1, 1, 1, 2, 2, 2, 3, 4, 5
The counsellor considers a median of 2 or more siblings as an indicator that students may benefit from a shared-experience peer support group.
Number of siblings: 0, 0, 1, 1, 1, 2, 2, 2, 3, 4, 5
The counsellor considers a median of 2 or more siblings as an indicator that students may benefit from a shared-experience peer support group.
a
Calculate the median number of siblings. [1]
b
Advise the counsellor whether the peer support group should be formed, justifying your answer using the median. [1]
Solutions
2QuestionCalculating Mean Median and ModeAssessment Practice
6 marks~9 minCriterion D
A small business employs 10 people with the following monthly salaries (in dollars):
The highest salary belongs to the CEO.
The highest salary belongs to the CEO.
a
Calculate the mean monthly salary. [2]
b
Calculate the median monthly salary. [2]
c
The business owner claims the company offers "above-average salaries" to attract new employees, using the mean as evidence. Advise a job applicant which measure of central tendency they should rely on when assessing typical pay at this company, and justify your recommendation. [2]
Solutions
3QuestionComparing Data Sets Using AveragesAssessment Practice
8 marks~12 minCriterion C
A small business owner records daily sales (in dollars) over two weeks:
The owner claims that Week 1 was better because its mean daily sales are higher.
| Week 1 | 120 | 135 | 110 | 128 | 142 | 115 | 130 |
|---|---|---|---|---|---|---|---|
| Week 2 | 200 | 95 | 105 | 118 | 122 | 108 | 112 |
The owner claims that Week 1 was better because its mean daily sales are higher.
a
Calculate the mean daily sales for each week. Show your working. [2]
b
Explain why the mean may be a misleading measure for comparing these two weeks. Identify the specific value that distorts the comparison and support your answer with a calculation. [2]
c
Justify the use of the median as a more appropriate measure of central tendency for this comparison. Calculate the median for each week and explain what the results reveal. [2]
d
The owner is considering whether the exceptional sales day in Week 2 could repeat due to a planned promotion. Advise the owner on whether the median alone is sufficient to inform this decision, justifying which measure — or combination of measures — would lead to a better-informed conclusion. [2]
Solutions
4QuestionCalculating Mean Median and ModeAssessment Practice
8 marks~12 minCriterion B
A city transport authority records daily passenger counts (in thousands) at five stations over one week. The analyst notices that some stations show symmetric distributions while others do not.
Five data sets are provided:
Five data sets are provided:
| Set A | 3 | 5 | 7 | 9 | 11 |
|---|---|---|---|---|---|
| Set B | 2 | 4 | 6 | 8 | 10 |
| Set C | 1 | 3 | 5 | 7 | 9 |
| Set D | 4 | 5 | 6 | 7 | 8 |
| Set E | 0 | 2 | 4 | 6 | 8 |
a
Calculate the mean and median for each data set. Record your results as labelled rows, then describe one pattern you observe across all five sets. [3]
b
Justify why, for any symmetric data set with an odd number of terms, the mean and median must be equal, referring to the role of the central term. [3]
c
The analyst considers using the mean to represent a sixth station whose daily counts are 1, 2, 3, 4, 20 (thousands). Calculate the mean and median for this data set, then advise the analyst whether the mean or the median should be reported to the public, justifying your recommendation in context. [2]
Solutions
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