Question

Consider the following data

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

I. Mean of the data is $22.65$
II. Mean deviation of the data is $1.25$
III. Mean of the data is $21.65$
IV. Mean deviation of the data is $2.25$

• A. I and II are true
• B. II and III are true
• C. I and IV are true
• D. III and IV are true

Answer 1

Answer: (B)

Let us write the given data in tabular form and calculate the required values to find mean deviation about the mean as

$x_i$	$f_i$	$f_i{x}_i$	$|d_i|=|x_i-\bar{x}|=|x_i-21.65|$	$f_i|d_i|$
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		25.00

Mean $(\overline{x})=\frac{\sum f_i{x}_i}{\sum f_i}=21.65$
Hence, mean of the data is $21.65$
Mean deviation $=\frac{\sum f_i|x_i-\overline{x}|}{\sum f_i}$
$=\frac{25}{20}=1.25$