Question Based on Dispersion

Dispersion


Find out range and coefficient of range
Size:
5-10
10-15
15-20
20-25
25-30
Frequency:
4
9
15
30
40
(Sol: - 25, 0.71)
Find out range and coefficient of range
Marks:
20-29
30-39
40-49
50-59
60-69
No. of students:
8
12
20
7
3
(Sol: - 50, 0.562)
Calculate quartile deviation and its coefficient
Size:
Less than 32
32-34
34-36
36-38
38-40
40-42
Over 42
Frequency:
12
18
16
14
12
8
6
(Sol: - 2.85, 0.079)
Calculate the mean deviation from mean as well as from median and coefficient of mean deviation from the following data:
20, 22, 25,38,40,50,65,70,75
(Sol: - 17.78, 0.39, 17.22, 0.48)
Calculate the mean deviation from mean and its coefficient from the following data:
Marks:
0-10
10-20
20-30
30-40
40-50
No. of students:
5
8
15
16
6
(Sol: - 9.44, 0.349)
Calculate mean deviation from the median and its coefficient from the following data:
Size:
100-120
120-140
140-160
160-180
180-200
Frequency:
4
6
10
8
5
(Sol: - 20.03, 0.1309)
Calculate the standard deviation of following series:
7, 10, 12, 13,15,20,21,28,29,35 (using assumed mean method)
(Sol: - 8.76)
Calculate standard deviation from the following data
X:
3
4
5
6
7
8
9
F:
7
8
10
12
4
3
2
(Sol: - 1.602)
Calculate mean and standard deviation for the following data:
Marks:
0-10
10-20
20-30
30-40
40-50
50-60
60-70
70-80
No. of students:
5
10
20
40
30
20
10
4
(Sol: - 39.38, 15.69)
Calculate standard deviation of the following distribution (Take assumed mean =32.5)
Age:
20-25
25-30
30-35
35-40
40-45
45-50
No. of persons:
170
110
80
45
40
35
(Sol: - 7.94)
11.) Two automatic filling machines A and B are used to fill tea in 500gms. Cartons. A random sample of 100 cartons on each machine showed the following:
Tea contents (in gms.)
Machine A
Machine B
485-490
12
10
490-495
18
15
495-500
20
24
500-505
22
20
505-510
24
18
510-515
4
13
Comment on the performance of the two machines on the basis of average filing and dispersion. (Sol: - S.D1=7.14, S.D2=7.55)
12.) Mean and standard deviation of 100 items are calculated by a student as 50 and 5.But later on it was found that two items were taken as 40 and 50 instead of 60 and 30.find the correct mean and s.d
(Sol: - mean=50, S.D = 5.385)
13.) Two models of radio were subjected to a durability test and the results were as follows:
Life in years:
0-2
2-4
4-6
6-8
8-10
10-12
Model A
5
16
13
7
5
4
Model B
2
7
12
19
9
1
State which model has a longer average life and more uniformity
(C.V (A) = 54.9%, C.V (B) = 36.2%)

Student of Rai Business School- New Delhi

Sanjeev Kumar Singh