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

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

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

Value: 50, 60, 80 Frequency: 2, $f$, 3

Find $f$ so that the mode of this distribution is the class 15–20.

Class & Frequency:

0–5: 3
6–10: 5
11–15: 7
15–20: $f$
21–25: 6

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 is 25.

In a grouped frequency distribution the class intervals and frequencies are given. Find $f$ so that the mean is 60.

Class & Frequency:

40–49: 3
50–59: $f$
60–69: 4
70–79: 2

Given the grouped data below, determine $f$ so that the modal class is 30–40.

Class & Frequency:

0–10: 4
10–20: 9
20–30: 12
30–40: $f$
40–50: 11

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

Class & Frequency:

0–9: 5
10–19: 8
20–29: $f$
30–39: 7
40–49: 3

Find $f$ so that the median of the data below is 37.

Class & Frequency:

30–34: 3
35–39: $f$
40–44: 5

Given the grouped data below, find $f$ so that the mean is 47.

Class & Frequency:

10–19: 4
20–29: $f$
30–39: 6
40–49: 5
50–59: 2

In a frequency distribution, find $f$ so that the modal class is 50–59.

Class & Frequency:

10–19: 4
20–29: 6
30–39: 9
40–49: 8
50–59: $f$
60–69: 7

In the frequency table below, find $f$ so that the mode lies in the class 25–30.

Class & Frequency: $\begin{array}{c|c} \hline \text{Class} & \text{Frequency} \\ \hline 5-10 & 5 \\ 10-15 & 8 \\ 15-20 & 11 \\ 20-25 & 9 \\ 25-30 & f \\ 30-35 & 7 \\ \hline \end{array}$

In the distribution below, find $f$ so that the median is 28.

Class & Frequency:

10–19: 4
20–29: $f$
30–39: 6
40–49: 4

Determine $f$ so that the median of this distribution is 45.

Class & Frequency:

10–29: 8
30–49: $f$
50–69: 6
70–89: 4