The document contains 10 problems related to statistics concepts like mean, median, standard deviation, variance, etc. The problems involve calculating these measures from data provided in tables and using formulas to derive new statistics based on existing statistics. For example, problem 1 asks to calculate the average bonus paid to workers based on salary groups and bonus amounts provided. Problem 5 asks to calculate the average speed of an airplane flying around a square based on its speeds on each side.
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Mean standard deviation
1. ASSIGNMENT-2
1.
The following are the monthly salaries (in Rs.) of 30 employees in firm:
140
139
126
114
100
88
62
77
99
103
108
129
144
148
134
63
69
148
132
118
142
116
123
104
95
80
85
106
123
133
The firm gave bonus of Rs. 10, 15, 20, 25, 30, and 35 for individuals in the respective
salary groups: ‘exceeding Rs 60 but not exceeding Rs 75’ ; ‘exceeding Rs.75 but not
ExceedingRs.90’; and so on up to ‘exceeding Rs.135 but not exceeding Rs.150’. Find the
average bonus paid worker.
2 Find out the missing frequencies of the following data, given that A.M. IS 67.45 inches
Height (inches) 60-62
No. of students
5
63-65
18
66-68
f1
69-71
f2
72-74
8
Total
100
3.The G.M. of 4 observations is 47, and the G.M. of 6 others is 40. Find the G.M.of all
the observations.
4. The geometric mean of six numbers is 75. If the geometric mean of four of them is
67,what is the geometric mean of the other two?
5. An aeroplane flies around a square the sides of which measure 100 Kms. each. The
aeroplane covers at a speed of 100Kms.per hour the first side, at 200 Kms.per hours the
second side, at 300 Kms. per hour the third side, and at 400Kms. per hour the fourth side.
Use the correct mean to find the average speed round the square.
6. The G.M., H.M. and A.M. of three observations are 3.63,3.27 and 4 respectively. Find
the observations.
7.Using a suitable formula calculate the median value from the following data:
Midvale
Frequency
115
6
125
25
135
48
145
72
155
116
165
60
175
38
185
22
195 Total
3
390
8. In a group of 1000 wage earns the monthly wages of 4% are below Rs.60 and those of
15% are under Rs. 62.50. 15% earned Rs95 and over, and 5% got Rs.100 and over. Find
the median wage.
ASSIGNMENT-3
1.Find out the range of the following data:
Height (inches)
40-49
50-59
60-69
70-79
80-89
2. No, of. Students
3
5
7
8
9
2.Calculate mean deviation from median from the following:
Class Boundary
Frequency
2-4
3
4-6
4
6-8
2
8-10
1
3.Find mean and standard deviation of ‘n’ natural numbers.
4. The mean and standard deviation of a group of 100 observations were found to be 20
and 3 respectively. After the calculations were made it was found that three of the
observations were incorrect which were recorded as 21, 21, and 18. Find the mean and
s.d. if the incorrect observations are omitted.
5. Ā is the mean of A1, A2, and A3. If a1, a2, a3 are the deviations of A1,A2, A3 from Ā
respectively, prove that
a12 +a22 + a32 = A12 +A22 + A32 – 3Ā 2.
6. If d2= mean square deviation about x, σ =standard deviation, and x-x = a, then show
that d2 = a2 + σ2.
7. Compute the s.d. of income from the following:
Income (Rs.)
No.of earners:
Below 200
25
200-399
72
400-599
47
600-799
22
800-999
13
1000-1199
7
8.Out of 400 observations, 100 observations have the value one and the rest of the
observations are zero. Find the mean and s.d. of 400 observations together.
9. The mean and the variance calculated from a group of 80 observations are 63.2 and
25.93 respectively. If 60 of these observations have mean 64.8 and s.d. 4, find the mean
and the s.d. of the remaining 20 observations.
10. The mean life in days and standard deviation for two types of electric bulbs are
given below:
Mean life in days
Standard deviation in days
Type I
310
9
Type II
260
14