Question Type 4: Finding the value of the frequency of a specific class with some condition on mean, median or mode Exercises

The following table shows the grouped frequency distribution for a set of data.

Find the value of $f$, given that the mean of the distribution is 33.5.

Find the smallest integer value of $f$ such that the mode of the following grouped data is in the class 20–29.

In the distribution below, find the value of $f$ such that the median of the distribution is 28.

A grouped frequency distribution is shown in the table below. Given that the mean of the distribution is $60$, find the value of $f$.

Calculate the frequency $f$ so that the mean of the data values in the following table is 65.

Find the minimum integer value of $f$ such that the modal class of this distribution is 16–20.

Determine the value of $f$ such that the median of the following frequency distribution is 45.

Given the grouped data below, find the minimum integer value of $f$ such that the modal class is $30\text{--}40$.

$\begin{array}{|c|c|} \hline \text{Class} & \text{Frequency} \\ \hline 0\text{--}10 & 4 \\ \hline 10\text{--}20 & 9 \\ \hline 20\text{--}30 & 12 \\ \hline 30\text{--}40 & f \\ \hline 40\text{--}50 & 11 \\ \hline \end{array}$

A frequency distribution has classes 0–9, 10–19, 20–29, 30–39, 40–49 with frequencies $5$, $f$, $10$, $8$, $2$. Find $f$ so that the mean of the distribution is $25$.

The following table shows a frequency distribution.

Find the minimum integer value of $f$ such that the modal class is $50\text{--}59$.

The following ungrouped data have frequencies $1$, $3$, $f$, $2$ and values $30$, $40$, $50$, $60$. Find $f$ so that the mean is $48$.