the median of the following frequency distribution is 49 and th
e total frequency is 100.find missing frequencies x and y class 0-10,10-20,20-30,40-50,50-60,60-70,70-80 and frequency 2,6,8,x,20,18,y,14
Answers
Answer:
Class interval Frequency Cumulative Frequency
0−10 5 5
10−20 f
1
5+f
1
20−30 20 25+f
1
30−40 15 40+f
1
40−50 f
2
40+f
1
+f
2
50−60 5 45+f
1
+f
2
N=60
From the table, it can be observed that N=60, then
2
N
=30.
45+f
1
+f
2
=60
∴ f
1
+f
2
=15 -------- ( 1 )
Median of the data is given as 28.5 which lies in interval 20−30.
∴ Median class =20−30
⇒ l=20,cf=5+f
1
,f=20,h=30−20=10.
⇒ Median=l+
f
2
N
−cf
×h
⇒ 28.5=20+
20
30−(5+f
1
)
×10
⇒ 8.5=
2
25−f
1
⇒ 17=25−f
1
∴ f
1
=8
From equation ( 1 ),
⇒ 8+f
2
=15
∴ f
2
=7
∴ The values of f
1
and f
2
are 8 and 7
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