The following table gives the distribution of the average weekly wages of $800$ workers in a factory. Calculate the median for the data given below.
Wages
( in hundreds) $20 - 25$ $25 - 30$ $30 - 35$ $35 - 40$ $40 - 45$ $45 - 50$ $50 - 55$ $55 - 60$
No. of persons $50$ $70$ $100$ $180$ $150$ $120$ $70$ $60$

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Solution

Wages

No. of persons( $f_{i}$ )

Cumulative Frequency (c.f.)

20-25

50

50

25-30

70

120

30-35

100

220(c)

35-40

180(f)

400

40-45

150

550

45-50

120

670

50-55

70

740

55-60

60

800=n

$\frac{n}{2} = 400$
median $= l + \frac{h}{f} \times (\frac{n}{2} - c)$
$l = 35; h = 5; f = 180; c = 220$
median $= 35 + \frac{5}{180} \times (400 - 220)$
$= 40$
Therefore, median $= 40$

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Similar questions

Age	20−25	25−30	30−35	35−40	40−45	45−50	50−55	55−60
No. Persons	50	70	100	180	150	120	70	60

Age	20−25	25−30	30−35	35−40	40−45	45−50	50−55	55−60
Number of Students	50	70	100	180	150	120	70	60

Age	20−25	25−30	30−35	35−40	40−45	45−50	50−55	55−60
Number of Students	50	70	100	180	150	120	70	60

\begin{matrix} W a g e s i n R s & N o . o f w o r k e r s 45 - 50 & 5 50 - 55 & 8 55 - 60 & 30 60 - 65 & 25 65 - 70 & 14 70 - 75 & 12 75 - 80 & 6 \end{matrix}

Weekly wages (in Rs.)	$50 - 55$	$55 - 60$	$60 - 65$	$65 - 70$	$70 - 75$	$75 - 80$	$80 - 85$	$85 - 90$
No. of workers	$5$	$20$	$10$	$10$	$9$	$6$	$12$	$8$

R s . 80

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Wages ( in hundreds)	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$	$45 - 50$	$50 - 55$	$55 - 60$
No. of persons	$50$	$70$	$100$	$180$	$150$	$120$	$70$	$60$