Question

Find the mean, median and mode for the following frequency table.

x	$10$	$20$	$25$	$30$	$37$	$55$
f	$5$	$12$	$14$	$15$	$10$	$4$

Answer 1

Find table

$x$ $f$ $xf$ $c.f.$

10 5 50 5

20 12 240 17

25 14 350 31

30 15 450 46

37 10 370 56

55 14 770 70

177 2230

Then, mean $=\frac{\Sigma xf}{\Sigma x}=\frac{2230}{177}=12.60$

Here $N=70$ then $\frac{70}{2}=35$

In the table, cumulative frequency greater than $35$ is $46$ where $x=30$

Then, median is $30$.

In the given table, greatest frequency is $15$ where value of $x=30$

Hence, mode is $30$