Exercises for Question Type 3: Finding the quartiles using the cumulative frequency graph

Question 1

Use the cumulative frequency table below for 28 observations to find the first quartile, third quartile and interquartile range. Value x Cum. Freq. 00841611241932254028

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Question 2

Estimate the quartiles and interquartile range from a cumulative frequency distribution table using linear interpolation.

A large survey yields the following cumulative frequency distribution for 150 responses: Score x Cumulative frequency 0020184055609580132100150 Estimate the first quartile, the third quartile, and the interquartile range.

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Question 3

A cumulative frequency curve for a sample of 80 observations has the following table of values: Boundary Cum. Freq. 00551515304050658080 Use this curve to estimate the first and third quartiles and the interquartile range.

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Question 4

The cumulative frequency distribution for 45 test scores is given by: Score x Cumulative frequency 501552515353045405545 Estimate Q_{1}, Q_{3} and the interquartile range.

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Question 5

A cumulative frequency table for 36 measurements is shown below. Use it to estimate Q_{1}, Q_{3} and the interquartile range. Value x Cum. Freq. 00631210181824283036

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Question 6

The following cumulative frequency table shows the waiting times, t minutes, of 24 customers. t Cumulative frequency 00521061512201825223024 Estimate the values of the lower quartile (Q_{1}), the upper quartile (Q_{3}), and the interquartile range (IQR).

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Question 7

The cumulative frequency table below summarises 60 observations. Estimate the lower quartile, upper quartile and interquartile range. Value x Cumulative frequency 0010420153030404550556060

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Question 8

The cumulative frequency distribution for daily sales (in units) of a store over 20 days is given below: Sales S Cumulative frequency 5010215520122520 Estimate Q_{1}, Q_{3} and compute the interquartile range, showing any interpolation.

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Question 9

The following table summarizes the cumulative frequency of test scores (in marks) for 12 students. Score x Cumulative frequency 1002033064095012 Find the lower quartile, the upper quartile and the interquartile range of the test scores.

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Question 10

The table below shows the cumulative frequency distribution for a sample of 50 measurements. Value x Cumulative frequency 0010420123028404050486050 Estimate the lower quartile (Q_{1}), the upper quartile (Q_{3}), and the interquartile range (I QR).

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Question 11

The cumulative frequency distribution of 100 customers’ ages is given in the table below: Age x Cumulative Frequency 10102025304540605075609070100 Estimate the lower quartile (Q_{1}), the upper quartile (Q_{3}), and the interquartile range (IQR).

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Question 12

Calculate estimates of the median and quartiles for grouped data, using a cumulative frequency curve or linear interpolation.

For 120 data points, the cumulative frequency table is as follows: Value x Cumulative Frequency 00101220353060509080110100120 Use this table to estimate Q_{1}, Q_{3} and the interquartile range (IQR).

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IB Mathematics Applications & Interpretation Question Type 3: Finding the Quartiles Using the Cumulative Frequency Graph Exercises