Name: Introduction to the Statistics
Uploaded: 2019-07-19
Duration: 4 min 50 s
Description: Statistics is a branch of Mathematics. In this video, we will learn the meaning of statistics and the classification of data. Let's watch this useful video t...

Question

Form a grouped distribution and calculate the median:

Marks	Number of students
Above $0$	$80$
Above $10$	$76$
Above $20$	$71$
Above $30$	$65$
Above $40$	$57$
Above $50$	$43$
Above $60$	$28$
Above $70$	$15$
Above $80$	$10$
Above $90$	$8$
Above $100$	$0$

Accepted Answer

Here, we have given more than cumulative frequency table.

First, we prepare the frequency table:

Marks Class interval Number of students Frequency $80$ Cumulative frequency $(c . f .)$

Above $0$ $0 - 10$ $80$ $80 - 76 = 4$ $4$

Above $10$ $10 - 20$ $76$ $76 - 71 = 5$ $5 + 4 = 9$

Above $20$ $20 - 30$ $71$ $71 - 65 = 6$ $6 + 9 = 15$

Above $30$ $30 - 40$ $65$ $65 - 57 = 8$ $8 + 15 = 23$

Above $40$ $40 - 50$ $57$ $57 - 43 = 14$ $14 + 23 = 37$

Above $57$ $50 - 60$ $43$ $43 - 28 = 15$ $15 + 37 = 52$

Above $60$ $60 - 70$ $28$ $28 - 15 = 13$ $13 + 52 = 65$

Above $70$ $70 - 80$ $15$ $15 - 10 = 5$ $5 + 65 = 70$

Above $80$ $80 - 90$ $10$ $10 - 8 = 2$ $2 + 70 = 72$

Above $90$ $90 - 100$ $8$ $8 - 0 = 8$ $8 + 72 = 80$

Above $100$ $100 - 110$ $0$ $0$ $0 + 80 = 80$

We have, $N = 80$

So, $\frac{N}{2} = \frac{80}{2} = 40$

The cumulative frequency just greater than $40$ is $52$ , which corresponds to the class $50 - 60$

Thus, the median class is $50 - 60$ .

Here, $l = 50$ (the lower limit of the median class)

$f = 15$ (frequency of the median class)

$h = 10$ (width of each class)

$N = 80$ (number of observations)

and $C = 37$ (cumulative frequency of class succeeding the median class)

$∴$ Median $= l + \frac{\frac{N}{2} - C}{f} \times h$

$= 50 + \frac{40 - 37}{15} \times 10$

$= 50 + \frac{3}{3} \times 2 = 50 + 2 = 52$

Hence, the median is $52$ .

Age (in years)	Number of policy holders
Below $20$	$2$
Below $25$	$6$
Below $30$	$24$
Below $35$	$45$
Below $40$	$78$
Below $45$	$89$
Below $50$	$92$
Below $0 + 80 = 80$	$98$
Below $60$	$100$

Class interval	$100 - 120$	$120 - 140$	$140 - 160$	$160 - 180$	$180 - 200$
Frequency	$12$	$14$	$8$	$6$	$10$

Daily expenditure (in $₹$ )	$100 - 150$	$150 - 200$	$200 - 250$	$250 - 300$	$300 - 350$
Number of workers	$6$	$7$	$12$	$3$	$2$

Daily income (in $₹$ )	$100 - 120$	$120 - 140$	$140 - 160$	$160 - 180$	$180 - 200$
Number of workers	$12$	$14$	$8$	$6$	$10$

Class interval	$0 - 4$	$5 - 9$	$10 - 14$	$15 - 19$	$20 - 24$
Number of students	$2$	$6$	$10$	$5$	$3$

Form a grouped distribution and calculate the median:

Marks Number of students

Above $0$ $80$

Above $10$ $76$

Above $20$ $71$

Above $30$ $65$

Above $40$ $57$

Above $50$ $43$

Above $60$ $28$

Above $70$ $15$

Above $80$ $10$

Above $90$ $8$

Above $100$ $0$

Important Questions on Statistics

Learn and Prepare for any exam you want !

Variable	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 80$
Frequency	$12$	$30$	_____	$65$	_____	$25$	$18$

Class interval	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	Total
Frequency	$8$	$16$	$36$	$34$	$6$	$100$

Form a grouped distribution and calculate the median: Marks Number of students Above 0 80 Above 10 76 Above 20 71 Above 30 65 Above 40 57 Above 50 43 Above 60 28 Above 70 15 Above 80 10 Above 90 8 Above 100 0

Important Questions on Statistics

Learn and Prepare for any exam you want !

Form a grouped distribution and calculate the median:

Marks Number of students

Above $0$ $80$

Above $10$ $76$

Above $20$ $71$

Above $30$ $65$

Above $40$ $57$

Above $50$ $43$

Above $60$ $28$

Above $70$ $15$

Above $80$ $10$

Above $90$ $8$

Above $100$ $0$