Find out mean deviation and its coefficient of the following data:

Items 5 10 15 20 25 30 35 40

Frequency 8 16 18 22 14 9 6 7

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Solution

Items (X) Frequency (f) fX Deviation from Mean
$|X - X|$ = $|d_{X}|$ $f |d_{X}|$

5
10
15
20
25
30
35
40 8
16
18
22
14
9
6
7 40
160
270
440
350
270
210
280 15.2
10.2
5.2
0.2
4.8
9.8
14.8
19.8 121.6
163.2
93.6
4.4
67.2
88.2
88.8
138.6

Σf = 100 Σfx = 2020 $Σ f |d X| = 765.6$

(a) $Mean (\bar{X}) = \frac{Σ f x}{Σ f} = \frac{2020}{100} = 20.2$

(b) Mean deviation from Arithmetic Mean

$M D_{X} = \frac{Σ f |d_{X}|}{Σ f} = \frac{765.6}{100} = 7.656$

(c) Coefficient of $M D_{\bar{X}}$ $= \frac{M D_{X}}{X} = \frac{7.656}{20.2} = 0.379 = 0.38 a p p r o x .$

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Class-Interval	0−5	5−10	10−15	15−20	20−25	25−30	30−35	35−40
Frequency	5	7	15	18	16	9	6	3

Variable	5−10	10−15	15−20	20−25	25−30	30−35
Frequency	2	9	29	54	11	5

Size	5−10	10−15	15−20	20−25	25−30	30−35	35−40	40−45	45−50
Frequency	6	10	18	30	15	12	10	6	4

Items	0−5	5−10	10−15	15−20	20−25	25−30	30−35	35−40
Frequency	2	5	7	13	21	16	8	3

Class Interval	1−5	6−10	11−15	16−20	21−25	26−30	31−35
Frequency	2	8	15	35	20	10	14