Statistics (Exercise 14.4) RD Sharma Solutions | Mathematics (Maths) Class 10 PDF Download

 Page 2


172 -174 
We have 
N = 420 
N/2 = 420/ 2 = 120 
171.5-174.5 18 
N =420 
420 
The cumulative frequency just greater than N/2 is 275 then 165.5 - 168.5 is the median class such, 
that 
L = 165.5, f = 142, F = 133 and h = 168.5 - 165.5 = 3 
li-F
Mean = L + N2-FfXhL + -
2
- x h
f 
= 166.5 + 1.63 = 168.13 
3. Following is the distribution of I.Q of 100 students. Find the median I.Q.
I.Q:
No of 
students: 
Soln: 
Class interval 
(exclusive) 
55- 64
65- 74
75- 84
85- 94
95-104
55-64 65-74 75-84 85-94 95-104 105-
1 
114 115-124 125-134 135-144
2 
22 
Class interval 
(inclusive) 
54.5-64-5 
64.5-74.5 
74.5-84.5 
84.5-94.5 
94.5-104.5 
9 
8 
22 
Class interval 
frequency 
1 
2 
9 
22 
33 (f) 
33 
2 1 
Cumulative 
frequency 
1 
3 
12 
34 (f) 
67 
Page 3


172 -174 
We have 
N = 420 
N/2 = 420/ 2 = 120 
171.5-174.5 18 
N =420 
420 
The cumulative frequency just greater than N/2 is 275 then 165.5 - 168.5 is the median class such, 
that 
L = 165.5, f = 142, F = 133 and h = 168.5 - 165.5 = 3 
li-F
Mean = L + N2-FfXhL + -
2
- x h
f 
= 166.5 + 1.63 = 168.13 
3. Following is the distribution of I.Q of 100 students. Find the median I.Q.
I.Q:
No of 
students: 
Soln: 
Class interval 
(exclusive) 
55- 64
65- 74
75- 84
85- 94
95-104
55-64 65-74 75-84 85-94 95-104 105-
1 
114 115-124 125-134 135-144
2 
22 
Class interval 
(inclusive) 
54.5-64-5 
64.5-74.5 
74.5-84.5 
84.5-94.5 
94.5-104.5 
9 
8 
22 
Class interval 
frequency 
1 
2 
9 
22 
33 (f) 
33 
2 1 
Cumulative 
frequency 
1 
3 
12 
34 (f) 
67 
Page 4


172 -174 
We have 
N = 420 
N/2 = 420/ 2 = 120 
171.5-174.5 18 
N =420 
420 
The cumulative frequency just greater than N/2 is 275 then 165.5 - 168.5 is the median class such, 
that 
L = 165.5, f = 142, F = 133 and h = 168.5 - 165.5 = 3 
li-F
Mean = L + N2-FfXhL + -
2
- x h
f 
= 166.5 + 1.63 = 168.13 
3. Following is the distribution of I.Q of 100 students. Find the median I.Q.
I.Q:
No of 
students: 
Soln: 
Class interval 
(exclusive) 
55- 64
65- 74
75- 84
85- 94
95-104
55-64 65-74 75-84 85-94 95-104 105-
1 
114 115-124 125-134 135-144
2 
22 
Class interval 
(inclusive) 
54.5-64-5 
64.5-74.5 
74.5-84.5 
84.5-94.5 
94.5-104.5 
9 
8 
22 
Class interval 
frequency 
1 
2 
9 
22 
33 (f) 
33 
2 1 
Cumulative 
frequency 
1 
3 
12 
34 (f) 
67 
Page 5


172 -174 
We have 
N = 420 
N/2 = 420/ 2 = 120 
171.5-174.5 18 
N =420 
420 
The cumulative frequency just greater than N/2 is 275 then 165.5 - 168.5 is the median class such, 
that 
L = 165.5, f = 142, F = 133 and h = 168.5 - 165.5 = 3 
li-F
Mean = L + N2-FfXhL + -
2
- x h
f 
= 166.5 + 1.63 = 168.13 
3. Following is the distribution of I.Q of 100 students. Find the median I.Q.
I.Q:
No of 
students: 
Soln: 
Class interval 
(exclusive) 
55- 64
65- 74
75- 84
85- 94
95-104
55-64 65-74 75-84 85-94 95-104 105-
1 
114 115-124 125-134 135-144
2 
22 
Class interval 
(inclusive) 
54.5-64-5 
64.5-74.5 
74.5-84.5 
84.5-94.5 
94.5-104.5 
9 
8 
22 
Class interval 
frequency 
1 
2 
9 
22 
33 (f) 
33 
2 1 
Cumulative 
frequency 
1 
3 
12 
34 (f) 
67