RevisionDojo

Question 1

Skill question

Construct a cumulative frequency graph for the data in the table:

\begin{array}{c|c} \text{Class interval} & \text{Frequency} \\ 10\text{--}20 & 5 \\ 20\text{--}30 & 8 \\ 30\text{--}40 & 7 \\ 40\text{--}50 & 4 \\ \end{array}

Plot the graph using the upper class boundaries.

Question 2

Skill question

Construct a cumulative frequency graph for the data in the table:

\begin{array}{c|c} \text{Class interval} & \text{Frequency} \\ 0\text{--}10 & 2 \\ 10\text{--}20 & 6 \\ 20\text{--}30 & 9 \\ 30\text{--}40 & 13 \\ 40\text{--}50 & 15 \\ \end{array}

Plot the curve using upper class boundaries.

Question 3

Skill question

The cumulative frequencies at the upper class boundaries for a data set are:

\begin{array}{c|c} \text{Upper class boundary} & \text{Cumulative frequency} \\ 10 & 8 \\ 20 & 18 \\ 30 & 30 \\ 40 & 40 \\ \end{array}

Construct the corresponding estimated frequency distribution table for the class intervals 0–10, 10–20, 20–30 and 30–40.

Question 4

Skill question

Construct a cumulative frequency graph for the following frequency distribution:

\begin{array}{c|c} \text{Class interval} & \text{Frequency} \\ 10\text{--}15 & 3 \\ 15\text{--}20 & 7 \\ 20\text{--}25 & 12 \\ 25\text{--}30 & 9 \\ 30\text{--}35 & 4 \\ \end{array}

Question 5

Skill question

A data set has the following frequency distribution with unequal class widths:

\begin{array}{c|c} \text{Class interval} & \text{Frequency} \\ 0\text{--}5 & 4 \\ 5\text{--}15 & 10 \\ 15\text{--}30 & 12 \\ 30\text{--}50 & 6 \\ \end{array}

Construct the cumulative frequency graph by plotting at the upper class boundaries.

Question 6

Skill question

The upper class boundaries and cumulative frequencies for a data set are:

\begin{array}{c|c} \text{Upper class boundary} & \text{Cumulative frequency} \\ 5 & 3 \\ 10 & 9 \\ 15 & 17 \\ 20 & 24 \\ 25 & 30 \\ \end{array}

Construct the estimated frequency distribution table for the class intervals 0–5, 5–10, 10–15, 15–20 and 20–25.

Question 7

Skill question

Use the cumulative frequency data below to estimate the first and third quartiles and hence find the interquartile range:

\begin{array}{c|c} \text{Value} & \text{Cumulative frequency} \\ 5 & 3 \\ 10 & 8 \\ 15 & 15 \\ 20 & 21 \\ 25 & 25 \\ \end{array}

Question 8

Skill question

A cumulative frequency table for exam scores is given by:

\begin{array}{c|c} \text{Upper score} & \text{Cumulative frequency} \\ 10 & 5 \\ 20 & 15 \\ 30 & 28 \\ 40 & 40 \\ 50 & 50 \\ \end{array}

Find the frequency for each 10‐point interval: 0–10, 10–20, 20–30, 30–40, 40–50.

Question 9

Skill question

The cumulative frequency distribution for the time to complete a task (in minutes) is:

\begin{array}{c|c} \text{Time (minutes)} & \text{Cumulative frequency} \\ 10 & 6 \\ 20 & 18 \\ 30 & 34 \\ 40 & 46 \\ 50 & 50 \\ \end{array}

Using linear interpolation within each class interval, estimate the first quartile, median and third quartile, and hence calculate the interquartile range.

Question 10

Skill question

Given the cumulative frequencies at certain upper bounds:

\begin{array}{c|c} \text{Upper class boundary} & \text{Cumulative frequency} \\ 20 & 7 \\ 30 & 18 \\ 40 & 31 \\ 50 & 45 \\ 60 & 60 \\ \end{array}

Determine the frequency for each class interval: 0–20, 20–30, 30–40, 40–50, 50–60.

Question 11

Skill question

The following cumulative frequency distribution shows the number of customers served in a shop over different time intervals:

\begin{array}{c|c} \text{Time (minutes)} & \text{Cumulative frequency} \\ 20 & 8 \\ 40 & 22 \\ 60 & 37 \\ 80 & 48 \\ 100 & 50 \\ \end{array}

Use linear interpolation to estimate Q1, the median and Q3, and hence calculate the interquartile range.

Question 12

Skill question

For a dataset with unequal class widths, the cumulative frequency distribution is:

\begin{array}{c|c} \text{Upper class boundary} & \text{Cumulative frequency} \\ 4 & 3 \\ 9 & 10 \\ 15 & 22 \\ 20 & 30 \\ 25 & 35 \\ \end{array}

Estimate the first quartile, median, third quartile and calculate the interquartile range using linear interpolation.

Question Type 2: Constructing cumilative frequency graphs given the frequency distribution table Exercises