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Measures of Central Tendency — Free MYP4 Mathematics (Standard) Practice Questions
1QuestionChoosing the Appropriate MeasureAssessment Practice
2 marks~3 minCriterion D
A hospital records the annual salaries (in thousands of dollars) of its staff. The distribution is right-skewed due to a small number of highly paid specialists.
Explain what the relationship reveals about this salary distribution, and justify which measure of central tendency the hospital should report to best represent a typical staff salary. [2]
Explain what the relationship reveals about this salary distribution, and justify which measure of central tendency the hospital should report to best represent a typical staff salary. [2]
Solutions
2QuestionMean from a Frequency TableAssessment Practice
6 marks~9 minCriterion C
A city planner is analysing household income data from a small town to decide where to locate a new community centre. The data are summarised below.
| Income range (thousand dollars per year) | 10–30 | 30–50 | 50–70 | 70–90 | 90–110 | 110–130 | 130–150 |
|---|---|---|---|---|---|---|---|
| Number of households | 45 | 62 | 38 | 20 | 12 | 8 | 5 |
a
Estimate the mean annual household income. Use the midpoint of each interval as the representative value. [2]
b
Evaluate whether the mean is an appropriate measure of central tendency for this dataset. In your response, identify the shape of the distribution and compare the mean with the median as a basis for deciding where to locate the community centre. [2]
c
The planner receives a second dataset for a neighbouring town in which the exact income of every household is recorded. Advise the planner whether to base the location decision on the grouped data from this town or the exact data from the neighbouring town, justifying your recommendation with reference to the reliability of each dataset. [2]
Solutions
3QuestionComparing Data Sets Using AveragesAssessment Practice
6 marks~9 minCriterion A
A city's environmental agency monitors daily air quality scores over five days.
Set A (recorded scores):
Due to a calibration improvement, every score in a revised data set, Set B, is exactly points higher than the corresponding score in Set A, giving values .
Set A (recorded scores):
Due to a calibration improvement, every score in a revised data set, Set B, is exactly points higher than the corresponding score in Set A, giving values .
a
Calculate the mean air quality score for Set A.
b
Show that the mean of Set B equals .
c
The agency considers air quality "satisfactory" if the mean score is at least . The minimum integer value of for which Set B meets this standard is . Justify whether this calibration adjustment is sufficient to conclude that the original instrument was under-reading by exactly units.
Solutions
4QuestionReal-Life Interpretation of AveragesAssessment Practice
6 marks~9 minCriterion B
A technology company records the following salary data for its employees.
A second company advertises a mean salary of 50 000 USD to attract new hires. Its salary data are:
| Salary (USD) | 30 000 | 40 000 | 50 000 | 60 000 | 70 000 |
|---|---|---|---|---|---|
| Number of employees | 3 | 7 | 12 | 5 | 3 |
A second company advertises a mean salary of 50 000 USD to attract new hires. Its salary data are:
| Salary (USD) | 35 000 | 45 000 | 55 000 | 65 000 |
|---|---|---|---|---|
| Number of employees | 4 | 6 | 8 | 2 |
a
Calculate the mean salary for the first company. [2]
b
Deduce the general formula for the weighted mean of a dataset where each value occurs with frequency , using the structure of your working in part (a) to guide your reasoning. [2]
c
Using your formula from part (b), calculate the mean salary for the second company, then advise a prospective employee whether the advertised figure of 50 000 USD gives a reliable picture of typical earnings at that company. Justify your answer. [2]
Solutions
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