Name: Scatter Graphs
Uploaded: 2019-07-19
Duration: 6 min 43 s
Description: Scatter plots are a powerful method of visualising relations between sets of numeric values. In this video, we will learn to construct a scatter plot.

Question

The monthly expenditure on milk in $200$ families of Housing Society is given below:

The monthly expenditure in ₹	$1000 - 1500$	$1500 - 2000$	$2000 - 2500$	$2500 - 3000$	$3000 - 3500$	$3500 - 4000$	$4000 - 4500$	$4500 - 5000$
The number of families	$24$	$40$	$33$	$x$	$30$	$22$	$16$	$7$

Find the value of $x$ and also, find the median and mean expenditure on milk.

Accepted Answer

Given,

The total number of families $= 200$

$\Rightarrow 24 + 40 + 33 + x + 30 + 22 + 16 + 7 = 200$

$3000 - 3500$

Expenditure (in $₹$ )

No. of families

$f_{i}$

Mid value

$40$ $x_{i}$

$x_{i} \times f_{i}$
C.F.

$1000 - 1500$ $24$ $1250$ $30000$ $24$

$1500 - 2000$ $40$ $1750$ $70000$ $64$

$2000 - 2500$ $33$ $2250$ $74250$ $97$

$2500 - 3000$ $28$ $2750$ $77000$ $125$

$3000 - 3500$ $30$ $3250$ $97500$ $155$

$3500 - 4000$ $22$ $3750$ $82500$ $177$

$4000 - 4500$ $40$ $33$ $x$ $30$

$4500 - 5000$ $7$ $4750$ $33250$ $200$

$\sum f_{i} = 200$ $\sum f_{i} x_{i} = 532500$

Mean $= \frac{\sum f_{i} x_{i}}{\sum f_{i}}$

$= \frac{532500}{200} = ₹ 2662.5$

$\frac{N}{2} = \frac{200}{2} = 100^{t h}$

$100^{t h}$ observation lies in class $2500 - 3000$ which is known as median class.

$l =$ lower limit of median class $= 2500$

$N =$ number of families $= 200$

$f =$ frequency of median class $= 28$

$C F =$ cumulative frequency of the class preceding the median class $= 97$

$h =$ class size $= 500$

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

$= 2500 + \frac{(\frac{200}{2} - 97)}{28} \times 500$

$= 2500 + \frac{(100 - 97)}{28} \times 500$

$= 2500 + \frac{3}{28} \times 500 = 2500 + 53.571 = 2553.571$

Hence, this is the required answer.

Class	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$
Frequency	$10$	$15$	$12$	$20$	$9$

Marks below	$10$	$20$	$30$	$40$	$50$	$60$
Number of students	$3$	$12$	$27$	$57$	$75$	$80$

Mass (in grams)	$80 - 100$	$100 - 120$	$120 - 140$	$140 - 160$	$160 - 180$
Number of apples	$20$	$60$	$70$	$x$	$60$

Mass (in $g$ )	$80 - 100$	$100 - 120$	$120 - 140$	$140 - 160$	$160 - 180$
Number of apples	$20$	$60$	$70$	$x$	$60$

Important Questions on Statistics

Learn and Prepare for any exam you want !

Monthly Expenditure(in $₹$ )	$1000 - 1500$	$1500 - 2000$	$= \frac{532500}{200} = ₹ 2662.5$	$2500 - 3000$	$3000 - 3500$	$3500 - 4000$	$4000 - 4500$	$100^{t h}$
Number of families	$24$	$40$	$33$	$x$	$30$	$22$	$16$	$7$