Question

Calculate the average daily income (in ₹) of the following data about men working in a company:

Daily income	$<100$	$<200$	$<300$	$<400$	$<500$
Number of men	12	28	34	41	50

Answer 1

Hint: The average value is the middle value of the set of data, and it is just calculated by the sum of all the values and dividing it by the total of all the values.
The average is also known as an arithmetic mean or mean of the two numbers, more than two numbers or the given data.
The mean is defined by the formula:
Average $=\dfrac{1}{n}\sum\limits_{i=0}^{n}{{{a}_{i}}=}\dfrac{{{a}_{1}}+{{a}_{2}}+{{a}_{3}}+{{a}_{4}}+.......+{{a}_{n}}}{n}$.
For example: find the average of 23,12,13,41,9,1
To find the average value just add all number and divide them by 6
$\Rightarrow \dfrac{23+12+13+41+9+1}{6}$
$\Rightarrow \dfrac{99}{6}$
$\Rightarrow 16.5$
Hence 16.5 is an average value of 23,12,13,41,9,1.

Complete step by step solution:
The data is given below:

Daily Income	Class	${{x}_{i}}$	${{f}_{i}}$	${{x}_{i}}{{f}_{i}}$
$<100$	$0-100$	50	12	600
$<200$	$100-200$	150	$28-12=16$	2400
$<300$	$200-300$	250	$34-28=6$	1500
$<400$	$300-400$	350	$41-34=7$	2450
$<500$	$400-500$	450	$50-41=9$	4050
	Total		$\sum{{{f}_{i}}=50}$	$\sum{{{x}_{i}}{{f}_{i}}=11,000}$

We know that Mean $=\sum{\dfrac{{{x}_{i}}{{f}_{i}}}{{{x}_{i}}}}$
$\Rightarrow \sum{\dfrac{{{x}_{i}}{{f}_{i}}}{{{x}_{i}}}}=\dfrac{11,000}{50}$
$\Rightarrow \dfrac{11,000}{50}=220$
$\Rightarrow 220$

Hence the average income is Rs 220.

Note:
The Mean or Average is found by using all the data
1) The mean is less than the mode.
2) The mean is also used in statistics such as the variance.
3) The average value is affected by high or low value.