A survey was conducted in a small industrial plant having $50$ workers to find the number of $k m$ each person commuted to work and the details are given below. Represent it by a histogram and frequency polygon.
Commuted Distance $(k m)$ $50 - 59$ $40 - 49$ $30 - 39$ $20 - 29$ $10 - 19$
No. of Workers $4$ $5$ $9$ $18$ $14$

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Solution

In the given table the class intervals are inclusive. So we convert them to the exclusive form and arrange the class intervals in ascending order.
Commuted Distance $(k m)$ $9.5 - 19.5$ $19.5 - 29.5$ $29.5 - 39.5$ $39.5 - 49.5$ $49.5 - 59.5$
No. of Workers $14$ $18$ $9$ $5$ $4$

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Draw a histogram to represent the following frequency distribution.

\begin{matrix} A g e (i n y e a r s) & 20 - 29 & 30 - 39 & 40 - 49 & 50 - 59 & 60 a n d a b o v e N u m b e r o f & 38 & 27 & 86 & 46 & 3 w o r k e r s \end{matrix}

Wages (₹)	10−19	20−29	30−39	40−49	50−59
Number of Workers	8	9	12	11	6

Age (in years)	16-19	20-29	30-39	40-49	50-59	60-64
Frequency	15	46	49	32	28	14

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Commuted Distance $(k m)$	$50 - 59$	$40 - 49$	$30 - 39$	$20 - 29$	$10 - 19$
No. of Workers	$4$	$5$	$9$	$18$	$14$

Commuted Distance $(k m)$	$9.5 - 19.5$	$19.5 - 29.5$	$29.5 - 39.5$	$39.5 - 49.5$	$49.5 - 59.5$
No. of Workers	$14$	$18$	$9$	$5$	$4$