Name: Representative Values
Uploaded: 2019-07-19
Duration: 1 min 24 s
Description: If we carry a series of measurements, the representative value will be their average. Watch this video to learn more about representative values.

Question

Draw an ogive for the following distribution. Read the median from the graph, and verify the result by calculation. How many workers earned wages between $₹ 60$ and $₹ 72$ ?

Weekly wages (in $₹$ )	No. of workers	Weekly wages (in $₹$ )	No. of workers
$50 - 55$	$6$	$70 - 75$	$16$
$55 - 60$	$10$	$75 - 80$	$12$
$60 - 65$	$22$	$80 - 100$	$15$
$65 - 70$	$30$

Accepted Answer

For less than ogive curve, we have,

Weekly Wages No of workers Cumulative frequency Points

$50 - 55$ $₹$ $6$ $55, 6$

$55 - 60$ $10$ $16$ $60, 16$

$60 - 65$ $22$ $38$ $65, 38$

$65 - 70$ $30$ $68$ $70, 68$

$70 - 75$ $16$ $84$ $75, 84$

$75 - 80$ $12$ $96$ $80, 96$

$80 - 100$ $15$ $111$ $100, 111$

For more than ogive curve, we have,

Weekly Wages No of workers Cumulative frequency Points

$50 - 55$ $6$ $111$ $50, 111$

$55 - 60$ $10$ $105$ $55, 105$

$65 - 70$ $30$ $95$ $60, 95$

$65 - 70$ $30$ $73$ $65, 73$

$70 - 75$ $16$ $43$ $70, 43$

$75 - 80$ $12$ $27$ $75, 27$

$80 - 100$ $15$ $15$ $80, 15$

So, the curve we get,
``
Now from the intersection of these two curves, we draw a parallel line to $x -$ axis, and this line meets $y -$ axis at the point $54$ .

Now we draw a perpendicular line to the intersection point on $x -$ axis, which meets $x -$ axis on $68$ .
So, the coordinates of this intersection point is $(68, 54)$ .
Hence, the median from the graph we get is $68$ .

Now, we consider the table of frequency distribution,

Weekly wages No of workers Cumulative frequency

$50 - 55$ $6$ $6$

$55 - 60$ $10$ $16$

$60 - 65$ $22$ $38$

$65 - 70$ $30$ $68$

$70 - 75$ $16$ $84$

$75 - 80$ $12$ $96$

$80 - 100$ $15$ $111$

Here total frequency $N = 111$ .

So, the median class is $65 - 70$ as $\frac{N + 1}{2} = \frac{111 + 1}{2} = 56$ belongs to the cumulative frequency of this class interval ( $N$ is odd).
Lower limit of median class $l = 65$ .
Width of the median class interval $h = 5$ .
Cumulative frequency preceding median class frequency $C = 38$ .
Frequency of median class $f = 30$ .
Median $= l + h (\frac{\frac{N + 1}{2} - C}{f})$
$= 65 + 5 (\frac{56 - 38}{30}) = 65 + 5 (\frac{18}{30}) = 65 + \frac{90}{30} = 65 + 3 = 68$
Hence, the median is $68$ .

Now for the second part of the question, we draw a line from $72$ which meets less than ogive at the point $N$ . From $N$ if we draw a parallel line to $x -$ axis, it meets $y -$ axis at $69$ .
Similarly if we draw another line from $60$ , it meets less than ogive curve at $P$ . From $P$ if we draw a parallel line to $x -$ axis, it meets $y -$ axis at $16$ .
``
So, the workers who earned wages between $₹ 60$ to $₹ 70$ is $(69 - 16) = 53$ .
Hence, the number of workers are $53$ .

Marks	$1 - 10$	$11 - 20$	$21 - 30$	$31 - 40$	$41 - 50$	$80 - 100$
No. of candidates	$3$	$16$	$26$	$31$	$16$	$8$

Marks	No. of students	Marks	No. of students
Below $10$	$15$	Below $50$	$96$
Below $20$	$35$	Below $60$	$127$
Below $30$	$60$	Below $70$	$198$
Below $40$	$84$	Below $65 - 70$	$250$

I.Q.	$96$	$65 - 74$	$75 - 84$	$85 - 94$	$95 - 104$	$105 - 114$	$\frac{N + 1}{2} = \frac{111 + 1}{2} = 56$	$125 - 134$	$135 - 144$
Frequency	$1$	$2$	$9$	$22$	$33$	$22$	$8$	$2$	$1$

Expenditure	$0 - 10$	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$
Number of families	$N$	$?$	$27$	$?$	$69$

Marks	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$
No. of students	$3$	$7$	$13$	$25$	$40$	$14$	$10$

Important Questions on Statistics

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Pocket expenses	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$
No. of students	$10$	$16$	$30$	$42$	$50$	$30$	$16$	$12$

Expenditure	$100 - 150$	$150 - 200$	$200 - 250$	$250 - 300$	$300 - 350$	$350 - 400$	$400 - 450$	$450 - 500$
Number of workers	$25$	$40$	$33$	$28$	$30$	$22$	$16$	$8$

Class - interval	$100 - 150$	$150 - 200$	$200 - 250$	$250 - 300$	$300 - 350$
Frequency	$4$	$6$	$13$	$5$	$2$