RevisionDojo

Question 1

S.3.1 - Frequency tables and cumulative frequency graphs.

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

\begin{array}{c|c} \text{Class interval} & \text{Frequency} \\ \hline 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.

[5]

Question 2

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.

[3]

Question 3

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

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

Using linear interpolation within each class interval, estimate the first quartile ( $Q_1$ ), the median ( $M$ ), and the third quartile ( $Q_3$ ), and hence calculate the interquartile range (IQR).

[6]

Question 4

Construct a cumulative frequency graph for the following frequency distribution:

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

[4]

Question 5

A cumulative frequency table for exam scores is given by:

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

Find the frequency for each 10-point interval: $0\text{--}10$ , $10\text{--}20$ , $20\text{--}30$ , $30\text{--}40$ , and $40\text{--}50$ .

[5]

Question 6

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

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

Plot the curve using upper class boundaries.

[4]

Question 7

The following table shows the cumulative frequencies for a distribution at specific upper class boundaries.

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

Determine the frequency for each of the following class intervals: $0\text{--}20$ , $20\text{--}30$ , $30\text{--}40$ , $40\text{--}50$ , and $50\text{--}60$ .

[3]

Question 8

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.

[4]

Question 9

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} \\ \hline 20 & 8 \\ 40 & 22 \\ 60 & 37 \\ 80 & 48 \\ 100 & 50 \\ \end{array}

Use linear interpolation to estimate $Q_1$ , the median and $Q_3$ , and hence calculate the interquartile range.

[7]

Question 10

The cumulative frequencies at the upper class boundaries for a data set are given in the following table:

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

Construct the corresponding estimated frequency distribution table for the class intervals $0 \text{--} 10$ , $10 \text{--} 20$ , $20 \text{--} 30$ and $30 \text{--} 40$ .

[4]

Question 11

For a dataset with unequal class widths, the cumulative frequency distribution is given in the following table:

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

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

[6]

Question 12

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} \\ \hline 5 & 3 \\ 10 & 8 \\ 15 & 15 \\ 20 & 21 \\ 25 & 25 \\ \end{array}

[5]

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