Calculate Standard Deviation and coefficient of variation from the following
data using Assumed Mean method.
Profits of companies (₹ in lakh) No. of companies
10-20 5
20-30 8
30-50 16
50-70 8
70-80 3
Answers
Explanation:
Profits of Companies (Rs. in lakhs)
Number of
Class-intervals
Companies frequencies
10 – 20
5
20 – 30
8
30 – 50
16
50 – 70
8
70 – 80
3
40
(i) Calculation of S.D. with the help of Actual Mean Method :
(1)
(2)
(3)
(4)
(5)
(6)
(7)
CI
f
m
fm
d
fd
fd2
10–20
5
15
75
–25.5
–127.5
3251.25
20–30
8
25
200
–15.5
–124.0
1922.00
30–50
16
40
640
–0.5
8.0
4.00
50–70
8
60
480
+19.5
+156.0
3042.00
70–80
3
75
225
+34.5
+103.5
3570.75
Σf=40
Σfm=1620
Σfd=0
Σfd2= 11790.00
(i) Calculation of S.D. with the help of Actual Mean Method :
(1)
(ii) Calculation of Standard Deviation by Assumed Mean Method :
(1)
(2)
(3)
(4)
(5)
(6)
CI
f
m
d
fd
fd2
10–20
5
15
–25
–125
3125
20–30
8
25
–15
–120
1800
30–50
16
40
0
0
0
50–70
8
60
+20
160
3200
70–80
3
75
+35
105
3675
Σf 40
Σfd=+20
Σfd2=11800
(i) Calculation of S.D. with the help of Actual Mean Method :
(1)
(iii) Calculation of Standard Deviation by Step Deviation Method :
(1)
(2)
(3)
(4)
(5)
(6)
(7)
CI
f
m
d
d'
fd'
fd'2
10–20
5
15
–25
–5
–25
125
20–30
8
25
–15
–3
-24
72
30–50
16
40
0
0
0
0
50-70
8
60
+20
+4
+32
128
70–80
3
75
+35
+7
+21
147
40
+4
472
(i) Calculation of S.D. with the help of Actual Mean Method :
(1)