Q.
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 $2 .25$
| Size | 20 | 21 | 22 | 23 | 24 |
| Frequency | 6 | 4 | 5 | 1 | 4 |
Statistics
Solution:
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 $=\frac{\sum f _{ i }\left| x _{ i }-\overline{ x }\right|}{\sum f _{ i }}$
$=\frac{25}{20}=1.25$
| $x_i$ | $f_i$ | $f_i x_i$ | $|d_i| = |x_i - \bar{x} | = |x_i - 21.65|$ | $f_i |d_i|$ |
|---|---|---|---|---|
| 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 |