Question 1: Calculate the mean Deviation about the median of the following observations:

(i) 3011, 2780, 3020, 2354, 3541, 4150, 5000

(ii) 38, 70, 48, 34, 42, 55, 63, 46, 54, 44

(iii) 34, 66, 30, 38, 44, 50, 40, 60, 42, 51

(iv) 22, 24, 30, 27, 29, 31, 25, 28, 41, 42

(v) 38, 79, 48, 34, 63, 42, 55, 44, 53, 47

Answer:

(i) 3011, 2780, 3020, 2354, 3541, 4150, 5000

3011	9
2780	240
3020	0
2354	666
3541	521
4150	1130
5000	1980
Total	4546

(ii) 38, 70, 48, 34, 42, 55, 63, 46, 54, 44

38	9
70	23
48	1
34	13
42	5
55	8
63	16
46	1
54	7
44	3
Total	86

(iii) 34, 66, 30, 38, 44, 50, 40, 60, 42, 51

34	9
66	23
30	13
38	5
44	1
50	7
40	3
60	17
42	1
51	8
Total	87

(iv) 22, 24, 30, 27, 29, 31, 25, 28, 41, 42

22	6.5
24	4.5
30	1.5
27	1.5
29	0.5
31	2.5
25	3.5
28	0.5
41	12.5
42	13.5
Total	47

(v) 38, 79, 48, 34, 63, 42, 55, 44, 53, 47

38	9.5
70	22.5
48	0.5
34	13.5
63	15.5
42	5.5
55	7.5
44	3.5
53	5.5
47	0.5
Total	84

Question 2: Calculate the mean deviation about the mean of the following observations:

(i) 4, 7, 8, 9, 10, 12, 13, 17

(ii) 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

(iii) 38, 70, 48, 40, 42, 55, 63, 46, 54, 44

(iv) 36, 72, 46, 42, 60, 45, 53, 46, 51, 49

(v) 57, 64, 43, 67, 49, 59, 44, 47, 61, 59

Answer:

(i) 4, 7, 8, 9, 10, 12, 13, 17

4	6
7	3
8	2
9	1
10	0
12	2
13	3
17	7
Total	24

(ii) 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

13	1
17	3
16	2
14	0
11	3
13	1
10	4
16	2
11	3
18	4
12	2
17	3
Total	28

(iii) 38, 70, 48, 40, 42, 55, 63, 46, 54, 44

38	12
70	20
48	2
40	10
42	8
55	5
63	13
46	4
54	4
44	6
Total	84

(iv) 36, 72, 46, 42, 60, 45, 53, 46, 51, 49

36	14
72	22
46	4
42	8
60	10
45	5
53	3
46	4
51	1
49	1
Total	72

(v) 57, 64, 43, 67, 49, 59, 44, 47, 61, 59

57	2
64	9
43	12
67	12
49	6
59	4
44	11
47	8
61	6
59	4
Total	74

Question 3: Calculate the mean deviation of the following income groups of fine and seven members from their medians:

I Income in Rs.	II Income in Rs.
4000	300
4200	4000
4400	4200
4600	4400
4800	4600
	4800
	5800

Answer:

1st Data Set

4000	400
4200	200
4400	0
4600	200
4800	400
Total	1200

2nd Data Set

300	4100
4000	400
4200	200
4400	0
4600	200
4800	400
5800	1400
Total	6700

Question 4: The lengths (in cm) of 10 rods in a shop are given below:

40.0, 52.3, 55.2, 72.9, 52.8, 79.0, 32.5, 15.2, 27.9, 30.2

(i) Find the mean deviation from median

(ii) Find mean deviation from the mean also.

Answer:

40	6.15
52.3	6.15
55.2	9.05
72.9	26.75
52.8	6.65
79	32.85
32.5	13.65
15.2	30.95
29.9	18.25
30.2	15.95
Total	166.4

40	5.98
52.3	6.32
55.2	9.22
72.9	26.92
52.8	6.82
79	33.02
32.5	13.48
15.2	30.78
27.9	18.08
32	13.98
Total	164.6

Question 5: In question 1 (iii), (iv), (v) find the number of observations lying between and , where M.D. is the mean deviation from the mean.

Answer:

34	11.5
66	20.5
30	15.5
38	7.5
44	1.5
50	4.5
40	5.5
60	14.5
42	3.5
51	5.5
Total	90

Also

Hence there are 6 observations between 36.5 and 54.5.

22	7.9
24	5.9
30	0.1
27	2.9
29	0.9
31	1.1
25	4.9
28	1.9
41	11.9
42	12.1
Total	48.8

Also

Hence there are 5 observations between 25.02 and 34.78.

38	11.4
70	20.6
48	1.4
34	15.4
63	13.6
42	7.4
55	5.6
44	5.4
53	3.6
47	2.4
Total