# The following table gives the marks obtained by 50 students in a class test: Calculate the mean, median and mode for the above data.

For equal class intervals, we will solve by finding mid points of these classes using direct method. We have got

Σfi = 47 and Σfixi = 1516

mean is given by   Thus, mean is 32.26.

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. We have got

So, N = 47

N/2 = 47/2 = 23.5

The cumulative frequency just greater than (N/2 = ) 23.5 is 29, so the corresponding median class is 30.5 - 35.5 and accordingly we get Cf = 15(cumulative frequency before the median class).

Now, since median class is 30.5 - 35.5.

l = 30.5, h = 5, f = 14, N/2 = 23.5 and Cf = 15

Median is given by,  = 30 + 3.03

= 33.03

Thus, median is 33.03.

Since, we have got mean = 32.26 and median = 33.03

Applying the empirical formula,

Mode = 3(Median) – 2(Mean)

Mode = 3(33.03) – 2(32.26)

Mode = 99.09 – 64.52 = 34.57

Mean = 32.26, Median = 33.03 and Mode = 34.57

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