Measures of Central Tendency
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Measures of Central Tendency — Free MYP5 Mathematics (Standard) Practice Questions

1QuestionCalculating Mean Median and ModeConcept Practice
2 marks~3 minCriterion A
A meteorologist records the daily maximum temperature (°C) in a coastal city over nn days, labelling each value x1,x2,x3,…,xnx_1, x_2, x_3, \ldots, x_n.

State the formula for the arithmetic mean xˉ\bar{x} of these nn values, using summation notation. [2]

Solutions

2QuestionChoosing the Appropriate MeasureAssessment Practice
4 marks~6 minCriterion D
A school librarian records the number of books read last month by 15 students.

Number of books (x)(x)1234520
Frequency (f)(f)433221
a
Calculate the mean number of books read. [1]
b
Determine the median number of books read. [1]
c
The librarian uses the mean to report the "typical" reading behaviour of the group. Advise the librarian whether the mean or the median is the more appropriate measure to use, justifying your answer with reference to the data. [2]
Question diagram

Solutions

3QuestionReal-Life Interpretation of AveragesAssessment Practice
4 marks~6 minCriterion C
A small company employs five people with monthly salaries (in euros) of 2 500, 3 000, 3 200, 3 500, and 4 000. After a performance review, every employee receives a bonus of 500 euros added to their salary.
a
Calculate the mean and median of the original salaries. [2]
b
Calculate the mean and median of the salaries after the bonus is added. [1]
c
The company director claims the bonus "makes salaries fairer by reducing the gap between the lowest- and highest-paid employees." Justify whether the mathematical evidence supports this claim. [1]
Question diagram

Solutions

4QuestionCalculating Mean Median and ModeAssessment Practice
6 marks~9 minCriterion B
A city's air-quality monitoring station records the daily Air Quality Index (AQI). The mean AQI for the first 5 days of a month is 12, and the AQI on day 6 is 18.
a
Calculate M6M_6, the mean AQI for the first 6 days. [2]
b
Deduce a general formula for Mn+1M_{n+1}, the mean of the first (n+1)(n+1) days, in terms of MnM_n, nn, and an+1a_{n+1}. Show all working. [2]
c
The AQI values for days 7 through 10 are 20, 15, 11, and 9. Health guidelines state that a monthly mean AQI above 13 triggers a public advisory. Using your formula from part (b), advise the monitoring station whether a public advisory should be issued after day 10. Justify your answer. [2]

Solutions

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