Class 11-commerce TR JAIN AND VK OHRI Solutions Statistics for Economics Chapter 9: Measures of Central Tendency- Arithmetic Mean
Measures of Central Tendency- Arithmetic Mean Exercise 176
Solution SAQ 1
Solution SAQ 2
Solution SAQ 3
|
Students |
Height (x) |
d = X - A |
|
A |
155 |
-7 |
|
B |
153 |
-9 |
|
C |
168 |
6 |
|
D |
160 |
-2 |
|
E |
162 = A |
0 |
|
F |
166 |
4 |
|
G |
164 |
2 |
|
H |
180 |
18 |
|
I |
157 |
-5 |
|
J |
165 |
3 |
|
|
∑X = 1630 |
∑d = 10 |
Solution SAQ 4
|
Weight (X) |
d = X - A |
|
20 |
-30 |
|
28 |
-22 |
|
34 |
-16 |
|
39 |
-11 |
|
42 |
-8 |
|
50 = A |
0 |
|
53 |
3 |
|
54 |
4 |
|
59 |
9 |
|
64 |
14 |
|
72 |
22 |
|
74 |
24 |
|
74 |
24 |
|
78 |
28 |
|
79 |
29 |
|
∑X = 820 |
∑d = 70 |
Measures of Central Tendency- Arithmetic Mean Exercise 177
Solution SAQ 5
|
Size (X) |
Frequency |
Deviation d = X-A |
fd |
|
30 |
2 |
5 |
10 |
|
29 |
4 |
4 |
16 |
|
28 |
5 |
3 |
15 |
|
27 |
3 |
2 |
6 |
|
26 |
2 |
1 |
2 |
|
25 = A |
7 |
0 |
0 |
|
24 |
1 |
-1 |
-1 |
|
23 |
4 |
-2 |
-8 |
|
22 |
5 |
-3 |
-15 |
|
21 |
7 |
-4 |
-28 |
|
|
∑f = 40 |
|
∑fd = -3 |
Solution SAQ 6
|
Marks (X) |
No. of Students (f) |
fx |
|
15 |
8 |
120 |
|
20 |
4 |
80 |
|
22 |
7 |
154 |
|
23 |
3 |
69 |
|
27 |
8 |
216 |
|
35 |
7 |
245 |
|
18 |
5 |
90 |
|
|
∑f = 42 |
∑fX = 974 |
Solution SAQ 7
|
Age (X) |
Mid-values (m) |
People (f) |
fm |
|
10 - 20 |
15 |
30 |
450 |
|
20 - 30 |
25 |
32 |
800 |
|
30 - 40 |
35 |
15 |
525 |
|
40 - 50 |
45 |
12 |
540 |
|
50 - 60 |
55 |
9 |
495 |
|
|
|
∑f = 98 |
∑fm = 2810 |
Solution SAQ 8
|
Class Interval |
Mid-values (m) |
Frequency (f) |
fm |
|
10 - 20 |
15 |
4 |
60 |
|
20 - 40 |
30 |
10 |
300 |
|
40 - 70 |
55 |
26 |
1430 |
|
70 - 120 |
95 |
8 |
760 |
|
120 - 200 |
160 |
2 |
320 |
|
|
|
∑f = 50 |
∑fm = 2870 |
Solution SAQ 9
|
Class Interval |
Mid- Value (m) |
Frequency (f) |
d = m-A |
fd |
|
20 - 25 |
22.5 |
10 |
-15 |
-150 |
|
25 - 30 |
27.5 |
12 |
-10 |
-120 |
|
30 - 35 |
32.5 |
8 |
-5 |
-40 |
|
35 - 40 |
37.5 = A |
20 |
0 |
0 |
|
40 - 45 |
42.5 |
11 |
5 |
55 |
|
45 - 50 |
47.5 |
4 |
10 |
40 |
|
50 - 55 |
52.5 |
5 |
15 |
75 |
|
|
|
∑f = 70 |
|
∑fd = -140 |
Solution SAQ 10
|
Items (x) |
Mid-Values (m) |
Frequency (f) |
d = m-A |
fd |
|
0 - 2 |
1 |
2 |
-4 |
-8 |
|
2 - 4 |
3 |
4 |
-2 |
-8 |
|
4 - 6 |
5 =A |
6 |
0 |
0 |
|
6 - 8 |
7 |
8 |
2 |
16 |
|
8 - 10 |
9 |
10 |
4 |
40 |
|
|
|
∑f = 30 |
|
∑fd = 40 |
Solution SAQ 11
Thus, average mean of the runs is 33.875
Solution SAQ 12
Let first and the last class intervals be (0- 10) and (60 - 70) respectively.
|
Class Interval |
Mid-Values (m) |
Frequency (f) |
fm |
|
0 - 10 |
5 |
5 |
25 |
|
10 - 20 |
15 |
12 |
180 |
|
20 - 30 |
25 |
18 |
450 |
|
30 - 40 |
35 |
22 |
770 |
|
40 - 50 |
45 |
6 |
270 |
|
50 - 60 |
55 |
4 |
220 |
|
60 - 70 |
65 |
3 |
195 |
|
|
|
∑f = 70 |
∑fm = 2110 |
Solution SAQ 13
Solution SAQ 14
Measures of Central Tendency- Arithmetic Mean Exercise 178
Solution SAQ 15
Solution SAQ 16
Solution SAQ 17
Solution SAQ 18
Thus, average income of remaining families is Rs 3378.95.
Solution SAQ 19
Thus, missing frequency is 16.
Solution SAQ 20
Solution SAQ 21
Solution SAQ 22
Solution SAQ 23
