# The following table gives the daily income of 50 workers of a factory: Find the mean, mode and median of the above data.

To find mean, we will solve by direct method: We have got

Σfi = 50 & Σfixi = 7260

mean is given by   To find median,

Assume Σfi = N = Sum of frequencies,

h = length of median class,

l = lower boundary of the median class,

f = frequency of median class

and Cf = cumulative frequency

Lets form a table. So, N = 50

N/2 = 50/2 = 25

The cumulative frequency just greater than (N/2 = ) 25 is 26, so the corresponding median class is 120 - 140 and accordingly we get Cf = 12(cumulative frequency before the median class).

Now, since median class is 120 - 140.

l = 120, h = 20, f = 14, N/2 = 25 and Cf = 12

Median is given by,  = 120 + 18.57

= 138.57

And we know that,

Mode = 3(Median) – 2(Mean)

= 3(138.57) – 2(145.2)

= 415.71 – 290.4

= 125.31

Hence, mean is 145.2, median is 138.57 and mode is 125.31.

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