A survey regardin

To find mean, we will solve by direct method:

We have got

Σf_i = 50 & Σf_ix_i = 7490

∵ mean is given by

⇒

⇒

To find median,

Assume Σf_i = N = Sum of frequencies,

h = length of median class,

l = lower boundary of the median class,

f = frequency of median class

and C_f = 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 C_f = 22(cumulative frequency before the median class).

Now, since median class is 150 - 160.

∴ l = 150, h = 10, f = 20, N/2 = 25 and C_f = 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.