Find the mean deviation about mean for the following data.
CI $0 - 5$ $5 - 10$ $10 - 15$ $15 - 20$ $20 - 25$ $25 - 30$ $30 - 35$ $35 - 40$ $40 - 45$ $45 - 50$
$f$ $9$ $13$ $6$ $12$ $9$ $6$ $10$ $15$ $6$ $4$

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Solution

Class interval

Frequency

Mid point $(x_{i})$

$f_{i} x_{i}$

$| x_{i} - ¯ x |$

$f_{i} (x_{i} - ¯ x)$

0-5

5-10

10-15

15-20

20-25

25-30

30-35

35-40

40-45

45-50

9

13

6

12

9

6

10

15

6

4

2.5

7.5

12.5

17.5

22.5

27.5

32.5

37.5

42.5

47.5

22.5

97.5

75.0

210

202.5

165

325

562.5

255

190

14.4

10.4

17.4

11.4

14.4

17.4

13.4

8.4

17.4

19.4

129.6

135.2

104.4

136.8

129.6

104.4

134

126

104.4

77.4

90

2105

144

1182

$¯ x = \frac{\sum f_{i} x_{i}}{\sum f} = \frac{2105}{90} = 234$
Mean Deviation obout Mean $= \frac{\sum f_{i} (x_{1} - M)}{\sum f_{i}} = \frac{1182}{90} = 13.13$

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Marks	0-5	5-10	10-15	15-20	20-25	25-30	30-35	35-40	40-45	45-50
Frequency	3	5	7	8	10	11	14	19	15	13

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

Variable( $x$ )	$10$	$15$	$20$	$25$	$30$	$35$	$40$	45
Frequency( $f$ )	$7$	$3$	$8$	$5$	$6$	$8$	$4$	9

Class:	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$
Frequency:	$5$	$6$	$15$	$10$	$5$	$4$	$2$	$2$

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CI	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$	$45 - 50$
$f$	$9$	$13$	$6$	$12$	$9$	$6$	$10$	$15$	$6$	$4$