Measures of Dispersion
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Measures of Dispersion — Free MYP5 Mathematics (Standard) Practice Questions

1QuestionBox and Whisker Plots for Spread of DataConcept Practice
4 marks~6 minCriterion A
A school's sports coordinator records the sprint times (in seconds) of 30 students during a fitness assessment. The box-and-whisker plot displays the results, with the following five-number summary:

Minimum =8.4= 8.4 s, Q1=10.2Q_1 = 10.2 s, Median =11.8= 11.8 s, Q3=13.6Q_3 = 13.6 s, Maximum =16.0= 16.0 s

Students who score within 4 seconds of the median are classified as "consistent performers."
a
Calculate the range of the sprint times. [1]
b
Calculate the interquartile range (IQR) of the sprint times. [1]
c
Justify whether the middle 50% of students qualify as consistent performers, using the IQR. [2]
Question diagram

Solutions

2QuestionCalculating the interquartile rangeAssessment Practice
4 marks~6 minCriterion C
A school tracks student performance on a standardised mathematics assessment. The box plot shows the distribution of scores for a class of 30 students. The minimum score is 4, the maximum is 40, Q1=12Q_1 = 12, the median =18= 18, and Q3=28Q_3 = 28.
a
Calculate the interquartile range (IQR). [1]
b
Analyse the symmetry of the distribution by calculating the distance from Q1Q_1 to the median and from the median to Q3Q_3. Hence deduce the direction of skew. [2]
c
The school's intervention policy states that the middle 50% of scores must span no more than 20 marks for the group to be considered "consistent." Justify whether this class meets the consistency criterion, and explain what the skewness suggests about the spread of scores in the lower half of the distribution. [1]
Question diagram

Solutions

3QuestionBox and Whisker Plots for Spread of DataAssessment Practice
6 marks~9 minCriterion D
A school uses exam scores from 120 students to decide whether to adjust its teaching programme. The box-and-whisker plot displays the distribution of scores with the following five-number summary:

Minimum =28= 28, Q1=55Q_1 = 55, Median =72= 72, Q3=88Q_3 = 88, Maximum =100= 100
a
Calculate the interquartile range (IQR) of the exam scores. [2]
b
Deduce the number of students whose scores fall within the interquartile range and the number whose scores fall within the upper whisker (from Q3Q_3 to the maximum). [2]
c
The school's policy states that a teaching programme requires adjustment if more than 30% of students score below Q1Q_1. Advise the school board whether the teaching programme requires adjustment, justifying your answer with reference to the data. [2]

Solutions

4QuestionRange and Interquartile RangeAssessment Practice
8 marks~12 minCriterion B
A city's air-quality monitoring network records daily fine-particle counts (µg/m³) at five sensors. On days following an industrial emission event, the highest reading rises progressively while the other four remain fixed:

Day 1: 2,4,6,8,102, 4, 6, 8, 10
Day 2: 2,4,6,8,1002, 4, 6, 8, 100
Day 3: 2,4,6,8,2002, 4, 6, 8, 200
Day 4: 2,4,6,8,5002, 4, 6, 8, 500
Day 5: 2,4,6,8,10002, 4, 6, 8, 1000
a
Calculate the range and interquartile range (IQR) for each of the five datasets. [2]
b
Deduce the range and IQR for the dataset 2,4,6,8,50002, 4, 6, 8, 5000, justifying your answer using the pattern observed in part (a). [2]
c
Calculate the range and IQR for the dataset 2,4,6,8,50002, 4, 6, 8, 5000 and verify whether your deduction in part (b) is correct. [2]
d
The health authority uses the IQR, not the range, to assess whether air-quality readings are "stable" across sensors. Advise the health authority whether this choice is sufficient for reliable stability assessment, using your results to support your recommendation. [2]

Solutions

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