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

Question 1

Skill question

Use the cumulative frequency table below for 28 observations to find the first quartile, third quartile and interquartile range.

$Value x Cum. Freq. 00841611241932254028$

[6]

Question 2

Skill question

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.

[6]

Question 3

Skill question

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.

[5]

Question 4

Skill question

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.

[6]

Question 5

Skill question

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

$Value x Cum. Freq. 00631210181824283036$

[5]

Question 6

Skill question

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).

[4]

Question 7

Skill question

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

$Value x Cumulative frequency 0010420153030404550556060$

[4]

Question 8

Skill question

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.

[5]

Question 9

Skill question

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.

[5]

Question 10

Skill question

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 ( $I QR$ ).

[6]

Question 11

Skill question

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).

[4]

Question 12

Skill question

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).

[6]

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

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