Question

The number of students absent in a class was recorded for 120 days and the information is given in the following frequency table.

No. of students absent (x)	0	1	2	3	4	5	6	7
No. of days (f)	1	4	10	50	34	15	4	2

Find the mean number of students absent per day.

Answer 1

First, take each class as ${x_i}$ and frequency ${f_i}$. The mean value is equivalent to the fraction between the addition of a product of mid-value with frequency and the total frequency.

Complete step-by-step answer:
We are given the number of students absent.
Let us assume that ${f_i}$ represents the number of days and ${x_i}$ is the number of students absent.
Mean is the measure of the average of a set of values which can be calculated by dividing the sum of all the observations by the number of observations.
The frequency distribution table for the given data is as follows:

${x_i}$	${f_i}$	${f_i}{x_i}$
0	1	0
1	4	4
2	10	20
3	50	150
4	34	136
5	15	75
6	4	24
7	2	14
$\sum {{f_i}} = 120$	$\sum {{f_i}{x_i}} = 423$

We know that the general formula to find the mean value is,
Mean $= \dfrac{{\sum {{x_i}{f_i}} }}{{\sum {{x_i}} }}$
Now, we will substitute the value for the sum of the product of frequency and midpoint and the value for the sum of total frequency.
$\Rightarrow$ Mean $= \dfrac{{423}}{{120}}$
Divide numerator by the denominator,
$\therefore$ Mean $= 3.525$

Hence the mean number of students absent per day is 3.525.

Note: In the mean formula, while computing $\sum {fx}$, don’t take the sum of $f$ and $x$ separately and then multiply them. It will be difficult. Students should carefully make the frequency distribution table; there are high chances of making mistakes while copying and computing data. The question is really simple, students should note down the values from the problem carefully, else the answer can be wrong. The other possibility of a mistake in this problem is while calculating as it has a lot of mathematical calculations.