Question

Find the mean deviation about the mean of the distribution:

Size	20	21	22	23	24
Frequency	6	4	5	1	4

• A. 1.25
• B. 2.5
• C. 3.75
• D. 4.5

Answer 1

Answer:

A. 1.25

Solution:

Given:

Size	20	21	22	23	24
Frequency	6	4	5	1	4

Concept used:

Mean = $\rm\frac{\sum f_i.x_i}{\sum f_i}$

Here,

x_i =Size, fi = Frequency

Calculation:

Size(xi)	Frequency(fi)	xi.fi
20	6	120
21	4	84
22	5	110
23	1	23
24	4	96
Total	20	433

 

So, mean = $\frac{433}{20}$

⇒ 21.65

Now,

To find the mean deviation we have to construct another table

Size(xi)	Frequency(fi)	xi.fi	di |xi - mean|	fi.di
20	6	120	1.65	9.90
21	4	84	0.65	2.60
22	5	110	0.35	1.75
23	1	23	1.35	1.35
24	4	96	2.35	9.40
Total	20	433	6.35	25.00

So, mean deviation =$\rm\frac{\sum f_i.x_i}{\sum f_i}$

⇒ $\frac{25}{20}$

⇒ 1.25

∴ The required answer is 1.25.