# A survey regarding the heights (in cm) of 50 girls of a class was conducted and the following data was obtained: Find the mean, median and mode of the above data.

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

Σfi = 50 & Σfixi = 7490

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 42, so the corresponding median class is 150 - 160 and accordingly we get Cf = 22(cumulative frequency before the median class).

Now, since median class is 150 - 160.

l = 150, h = 10, f = 20, N/2 = 25 and Cf = 22

Median is given by,  = 150 + 1.5

= 151.5

And we know that,

Mode = 3(Median) – 2(Mean)

= 3(151.5) – 2(149.8)

= 454.5 – 299.6

= 154.9

Hence, mean is 149.8, median is 151.5 and mode is 154.9.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.