Question

ind the median of the following data Class intervals Frequency 0-10 6 10-20 9 20-30 15 30-40 9 40-50 1 N= 40​

Answer 1

MEAN ;-

☆ To find the mean let us put the data in the table given below,

Mean of the given data is 24.

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MEDIAN ;-

☆ To find the median let us put the data in the table given below,

☆ The cumulative frequency just greater than 15, i.e. 20 and the corresponding class is 20-30.

♨ Thus the median class is 20-30.

I = Lower limit = 20

N = 30 & N/2 = 15

C.F = 12

f = Frequency = 8

h = Class interval = 30 - 20 = 10

Median of the given data is 23.75.

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MODE ;-

We Know that

☆ indigoMode= I + $\frac{f {1} - fo } {2f1 - fo - f2} \times h$

Where,

I = 20

f1 = Max${}^{m}frequency = 8$

$fo = 7$

$f2 = 6$

h = 10

:⟹ Mode $= 20 + \frac{8 - 7}{2 \times 8 - 7 - 6 } \times 10$

:⟹ Mode $= 20 + \frac{1}{16 - 13} \times 10$

:⟹ Mode $20 + \frac{10}{3}$

:⟹ Mode $= 20 + 3.32$

:⟹ limeMode $= 23.32$

Or

$we \: know \: that$

☆ $olive \: mode = (3 \times median) - (2 \times mean)$

:⟹ Mode $= 3 \times 23.75 - 2 \times 24$

:⟹ Mode $= 71.25 - 48$

:⟹ coralMode $= 23.25$

Mode of the given data is 23.32.

Answer 2

Mode of the given data is 23.32.

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