find the value of f1 and f2 of frequency if median is 26. 4 and the total frequency is 40. I Series are 0-8,8-16,16-24,24-32,32-40 frequency are 6,7,f1,8,f2
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1
Class interval Frequency Cumulative frequency
0−10 f
1
f
1
10−20 5 5+f
1
20−30 9 14+f
1
30−40 12 26+f
1
40−50 f
2
26+f
1
+f
2
50−60 3 29+f
1
+f
2
60−70 2 31+f
1
+f
2
N=40
⇒ Median=32.5, then 30−40 is class interval.
⇒ l=30,cf=14+f
1
,f=12 and h=40−30=10.
⇒ N=40,
2
N
=20
⇒ 31+f
1
+f
2
=40.
⇒ Then, f
1
+f
2
=9 ----- ( 1 )
⇒ Median=l+
f
2
N
−cf
×h
⇒ 32.5=30+
12
20−(14+f
1
)
×10
⇒ 2.5=
6
6−f
1
×5
⇒ 15=30−5f
1
⇒ 5f
1
=15
∴ f
1
=3
Substituting value in equation ( 1 ) we get,
⇒ 3+f
2
=9
∴ f
2
=6
∴ f
1
=3,f
2
=6
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