Calculate Mean Deviation from the following table using :
(i) Actual Mean Method
(ii) Assumed Mean Method
(iii) Step Deviation Method
|
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 |
(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 |
(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 |
