I.Q’s of 100 students are given in the following table: I.Q. Number of students Less than 120 10 Less than 130 29 Less than 140 64 Less than 150 78 Less than 160 90 Less than 170 100 Draw the “ less than type ogive” for the given data. Also , obtain the median from the curve
Answers
Answer:
Class interval Frequency Cumulative frequency
0−10 0 0
10−30 10 10
30−50 15 25
50−70 18 43
70−90 22 65
90−110 22 87
110−130 9 96
130−150 4 100
N=100
We have, N=100,
2
N
=50
The cumulative frequency just greater than
2
N
is 65 then median class is 70−90 such that,
l=70,h=90−70=20,f=22,cf=43
Median=l+
f
2
N
−cf
×h
⇒ Median=70+
22
50−43
×20
⇒ Median=70+
22
7×20
⇒ Median=70+6.36
∴ Median=76.36
(ii)
Class interval Frequency Cumulative Frequency
80−90 9 9
90−100 17 26
100−110 19 45
110−120 45 90
120−130 33 123
130−140 15 138
140−150 12 150
150−160 0 150
N=150
We have, N=150, then,
2
N
=
2
150
=75
The cumulative frequency just more than
2
N
is 90 then the median class is 110−120 such that
l=70,h=120−110=10,f=45,cf=45
Median=l+
f
2
N
−cf
×h
⇒ Median=110+
45
75−45
×10
⇒ Median=110+
45
30×10
⇒ Median=110+6.67
∴ Median=116.67
hope it's helpful to you
