if the median of the following data is 32.5 find the missing frequencies . C.I = 10-20, 20-30 , 30-40,40-50,50-60,60-70 . frequency = 3,x,9,12,y,3,2 . total = 40
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Answer:
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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