Question

obtain the mean of the following distribution:
variable(x)=4,6,8,10,12
frequency(f)=4,8,14,11,3​

Answer 1

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Mean = 8.05

Median = 8

Mode = 8

CALCULATION OF MEAN:

Frequency Table

x f fx

4 4 16

6 8 48

8 14 112

10 11 110

12 3 36

TOTAL 40 282

Mean = \frac{sum(fx)}{sum(f)}

sum(f)

sum(fx)

= 322/40

= 8.05

CALCULATION OF MEDIAN:

Given observations as per the given frequency are

4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12

N = 40

N + 1 = 40 + 1 = 41

(N+1)/2 = 20.5

Median = (N+1)/2th observation

= 8

CALCULATION OF MODE:

Mode = observation with highest frequency

= 8