Calculate median from the following data:
Marks less than:
80 70 60 50 40 30 20 10
No. of suudents:
100 90 80 70 60 32 20 13 5
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Answer:
ANSWER
CI cf f x
i
∣x
i
−M∣ f
i
∣x
i
−M∣
0−10 5 5 5 41.43 207.15
10−20 13 13−5=8 15 31.43 251.44
20−30 20 20−13=7 25 21.43 150.01
30−40 32 32−20=12 35 11.43 137.16
40−50 60 60−32=28 45 1.43 40.04
50−60 80 80−60=20 55 8.57 171.4
60−70 90 90−80=10 65 18.57 185.7
70−80 100 100−90=10 75 28.57 285.7
∑f
i
=100 ∑f
i
∣x
i
−M∣=1428.6
N=100, then,
2
N
=
2
100
=50
∴ Median class =40−50
Then we have, l=40,cf=32,f=28,h=10
Median(M)=l+
f
2
N
−cf
×h
=40+
28
50−32
×10
=40+6.43
=46.43
Mean deviation from median =
∑f
i
∑f
i
∣x
i
−M∣
=
100
1428.6
=14.286
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