Find x and y if the median of the following data is 31.
Class Interval Frequency
00-10 5
10-20 x
20-30 6
30-40 y
40-50 6
50-60 5
Total 40
Answers
Answer:
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Step-by-step explanation:
ANSWER
Classes Frequency c.f
0−10 5 5
10−20 x 5+x
20−30 6 11+x
30−40 y 11+x+y
40−50 6 17+x+y
50−60 5 22+x+y
Total 40
⇒ 22+x+y=40
∴ x+y=18 ----- ( 1 )
⇒ Here, median class =30−40
⇒ l=30,c.f=11+x,f=y,h=10,
2
n
=
2
40
=20
⇒ Median =31
Median=l+
⎣
⎢
⎡
f
2
n
−cf
⎦
⎥
⎤
×h
31=30+[
y
20−(11+x)
]×10
1=
y
9−x
×10
∴ 10x+y=90 ---- ( 2 )
Now, subtracting equation ( 1 ) from ( 2 ), we get
x=8 and
y=10
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