52. The mode of the following frequency distribution of 165 observation is 38:
Class
5-14 14-23 23-32 32-41 41-50 50-59 59-68
13
8
a
53
18
b
12
Frequency
Find the values of a and b.
Please give a swer if you can solve it
Answers
Answered by
1
Answer:
Here, modal class
=
32
−
41
⇒
l
=
32
,
f
0
=
a
,
f
1
=
53
,
f
2
=
b
and
h
=
9
⇒
M
o
d
e
=
l
+
f
1
−
f
0
2
f
1
−
f
0
−
f
2
×
h
⇒
34.5
=
32
+
53
−
a
2
×
53
−
a
−
b
×
9
⇒
2.5
9
=
53
−
a
106
−
a
−
b
⇒
265
−
2.5
a
−
2.5
b
=
477
−
9
a
⇒
7.5
a
−
2.5
b
=
212
⇒
75
a
−
25
b
=
2120
∴
13
a
−
5
b
=
424
------ ( 1 )
As total observation are
165
⇒
So,
5
+
11
+
a
+
53
+
b
+
16
+
10
=
165
⇒
95
+
a
+
b
=
165
∴
a
+
b
=
70
-------- ( 2 )
∴
b
=
70
−
a
Substitute
b
=
70
−
a
in equation ( 1 )
⇒
13
a
−
5
(
70
−
a
)
=
424
⇒
13
a
−
350
+
5
a
=
424
⇒
18
a
=
424
+
350
⇒
18
a
=
774
∴
a
=
43
⇒
b
=
70
−
43
=
27
∴
Frequency
a
=
43
and
b
=
27
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