IB Mathematics Applications & Interpretation Question Type 2: Constructing Cumilative Frequency Graphs Given the Frequency Distribution Table Exercises

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

$$\begin{array}{cc}\text{Class interval}& \text{Frequency}\\ 0\text{–}5& 4\\ 5\text{–}15& 10\\ 15\text{–}30& 12\\ 30\text{–}50& 6\end{array}$$

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

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

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

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

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

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

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

Construct a cumulative frequency graph for the following frequency distribution:

$$\begin{array}{cc}\text{Class interval}& \text{Frequency}\\ 10\text{–}15& 3\\ 15\text{–}20& 7\\ 20\text{–}25& 12\\ 25\text{–}30& 9\\ 30\text{–}35& 4\end{array}$$

A cumulative frequency table for exam scores is given by:

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

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

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

$$\begin{array}{cc}\text{Class interval}& \text{Frequency}\\ 0\text{–}10& 2\\ 10\text{–}20& 6\\ 20\text{–}30& 9\\ 30\text{–}40& 13\\ 40\text{–}50& 15\end{array}$$

Plot the curve using upper class boundaries.

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

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

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

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

$$\begin{array}{cc}\text{Class interval}& \text{Frequency}\\ 10\text{–}20& 5\\ 20\text{–}30& 8\\ 30\text{–}40& 7\\ 40\text{–}50& 4\end{array}$$

Plot the graph using the upper class boundaries.

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

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

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

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

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

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

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

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

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

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

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