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Question

Answer the following questions in detail−

Calculate Q1 and Q3 from the following data.
Class 10-20 20-30 30-40 40-50 50-60 60-70 70-80
Freq. 10 15 25 40 35 20 5

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Solution

C.I.
f
C.F.
10–20
10
10
20–30
15
25
30–40
25
50
40–50
40
90
50–60
35
125
60–70
20
145
70–80
5
150
150

Q1=N4th=1504th=57.5th

It falls in the 50th c.f

Now,

Q1=30-40Q1=L1+L2-L1fN4-cfQ1=30+40-30251504-25

Thus, we have:

Q1=35Q3=3N4th =3×1504th=112.5

This falls in the 125th c.f

Q3=50-60Q3=L1+L2-L1f3N4-cfQ3=50+60-50353×1504-90

Thus, we have:
Q3 = 56.42

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