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

$250$ apples of a box were weighed and the distribution of masses of the apples is given in the following table:

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

Find the value of $x$ , the mean mass of the apples and the modal mass of the apples.

Accepted Answer

Given, total number of apples $= 250$

$20 + 60 + 70 + x + 60 = 250$

$x = 250 - 210 = 40$

Mass (in grams) Number of apples $(f)$ Mid value $(x)$ $d = (x_{i} - A)$ $f \times d$

$80 - 100$ $20$ $90$ $- 40$ $- 800$

$100 - 120$ $60$ $110$ $- 20$ $- 1200$

$120 - 140$ $70$ $130 (A)$ $0$ $0$

$140 - 160$ $40$ $150$ $20$ $800$

$160 - 180$ $60$ $120 - 140$ $40$ $2400$

$\sum f = 250$ $60$

Now, mean $(\bar{x}) = A + \frac{\sum f d}{\sum f}$

$= 130 + \frac{1200}{250}$

$= 134.8$

Now, Mode $= l + \frac{f_{1} - f_{0}}{2 f_{1} - f_{0} - f_{2}} \times h$

Where $/ =$ lower class limit of modal class $= 12$

Modal class is $(120 - 140)$ , Since it consist highest frequency

$l = 120$

$h = class size = 20$

$f_{1} =$ frequency of modal class $= 70$

$f_{0} =$ frequency of class preceding the modal class $= 60$

$f_{2} =$ frequency of class succeeding the modal class $= 40$

$= 120 + (\frac{70 - 60}{2 \times 70 - 60 - 40}) \times 20$

$= 120 + \frac{10}{40} \times 20$

$= 120 + \frac{10}{2} = 125$

Class	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$l = 120$	$h = class size = 20$	$60 - 70$	$70 - 80$
Frequency	$f_{1}$	$5$	$= 60$	$12$	$f_{2}$	$= 40$	$2$	$40$

Marks	No. of students
$0 - 5$	$2$
$5 - 10$	$5$
$10 - 15$	$6$
$15 - 20$	$8$
$20 - 25$	$10$
$25 - 30$	$25$
$30 - 35$	$20$
$35 - 40$	$18$
$40 - 45$	$4$
$45 - 50$	$2$

Production yield $(kg / hec)$	$40 - 45$	$45 - 50$	$50 - 55$	$55 - 60$	$60 - 65$	$65 - 70$
Number of farms	$4$	$6$	$16$	$20$	$30$	$24$

Class	$0 - 100$	$100 - 200$	$200 - 300$	$300 - 400$	$400 - 500$	$500 - 600$	$600 - 700$	$700 - 800$	$800 - 900$	$900 - 1000$
Frequency	$2$	$5$	$x$	$12$	$17$	$20$	$y$	$9$	$7$	$4$

Important Questions on Statistics

Learn and Prepare for any exam you want !

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

250 apples of a box were weighed and the distribution of masses of the apples is given in the following table: Mass (in grams) 80-100 100-120 120-140 140-160 160-180 Number of apples 20 60 70 x 60 Find the value of x, the mean mass of the apples and the modal mass of the apples.

Important Questions on Statistics

Learn and Prepare for any exam you want !