Ogive 871 8. The median of the following data is 16. Find the missing frequencies a and b if the total of frequencies is 70. Class 0-5 5-10 10-15 15-20 20-25 25-30 30–35 35-40 Frequency 12 12 15 b 6 6 4 w [CBSE 2013] ] 9. In the following data the median of the runs scored hun а
Answers
Step-by-step explanation:
Class Interval Frequency cf0−512125−10a12+a10−151224+a15−201539+a20−25b39+a+b25−30645+a+b30−35651+a+b35−40455+a+b=70Here:
N=70
N/2=35
Median =16, Median class =15−20
So, I=15, h=5, f=15 and
xf=xf of preceding class i.e.24+a
We know,
Median =1+⎩⎪⎪⎪⎨⎪⎪⎪⎧h×f(2N−cf)⎭⎪⎪⎪⎬⎪⎪⎪⎫
Substitute all the value in the above formula, we get
16=15
Answer:
Class Interval Frequency cf
0−5 12 12
5−10 a 12+a
10−15 12 24+a
15−20 15 39+a
20−25 b 39+a+b
25−30 6 45+a+b
30−35 6 51+a+b
35−40 4 55+a+b=70
Here:
N=70
N/2=35
Median =16, Median class =15−20
So, I=15, h=5, f=15 and
xf=xf of preceding class i.e.24+a
We know,
Median =1+
⎩
⎪
⎪
⎪
⎨
⎪
⎪
⎪
⎧
h×
f
(
2
N
−cf)
⎭
⎪
⎪
⎪
⎬
⎪
⎪
⎪
⎫
Substitute all the value in the above formula, we get
16=15+{5×(35−24−a)/15}
⇒16=15+(11−a)/3
or a=8
Now, 70=55+a+b
70=55+8+b
⇒b=7
so, missing frequincies are 8 and 7.
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Step-by-step explanation:
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