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 
86.8 
Also
Hence there are 6 observations between 40.72 and 58.08.