The following table shows the weights of $20$ students. Calculate the mean, median and mode.
Weight(in kg) $47$ $50$ $53$ $56$ $60$
Number of students $4$ $3$ $7$ $2$ $4$

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Solution

Weight No. Of Students $(x)$ $x f$ $c f$
47 4 188 4
50 3 150 7
53 7 371 14
56 2 112 16
60 4 240 20
266 1061

Then, mean $= \frac{Σ x f}{Σ x} = \frac{1061}{266} = 3.99$
Here, $N = 20$ then $\frac{20}{2} = 10$
In the table, cumulative frequency greater then $10$ is $14$ where value of $x = 53$
Then, median is $53$
In the given table, greatest frequency is $7$ where value of $x = 53$ then mode is $53$ .

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Weight (in kg)	47	50	53	56	60
Number of students	4	3	2	2	4

Weight (Kg)	60	56	53	50	47
Number of students	4	2	2	3	4

40

Weight	$45$	$46$	$47$	$48$	$49$	$50$	$51$	$52$	$53$
Median	$6$	$2$	$3$	$4$	$7$	$4$	$7$	$4$	$3$

Weight (in kg)	40 - 44	44 - 48	48 - 52	52 - 56	56 - 60	60 - 64	64 - 68	68 - 72
Number of students	4	6	10	14	10	8	6	2

60

The following table gives the marks obtained by 50 students in a class test:

Marks	11−15	16−20	21−25	26−30	31−35	36−40	41−45	46−50
Number of students	2	3	6	7	14	12	4	2

Calculate the mean, median and mode for the above data.

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Weight(in kg)	$47$	$50$	$53$	$56$	$60$
Number of students	$4$	$3$	$7$	$2$	$4$