1.

Calculate the median from the following data: Marks below:1020304050607080 No. of students:1535608496127198250

Answer»
 140 Kg below No. of students Class interval Frequency Cumulative frequency
 10 150 - 10 15 15
 20 3510 - 20 20 35
 30 6020 - 30 25 60
 40 8430 - 40 24 84
 50 9640 - 5012 96 (F)
 60 12750 - 6031 (f) 127
 70 19860 - 7071 198
 80 25070 - 8052 250
 N = 250

We have, 

N = 250

\(\frac{N}{2}=\frac{250}{2}=125\)

The cumulative frequency is just greater than \(\frac{N}{2}\) is 127 then median class is 50-60 such that:

l = 50, f = 31, F = 96, h = 60-50 = 10

Median = I + \(\frac{\frac{N}{2}-F}{f}\)

\(=50+\frac{125-96}{31}\times 10\)

\(=50+\frac{29\times10}{31}\)

\(=\frac{445}{31}=59.35\)


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