The following table gives the daily wages of workers in a factory:
| Wages (₹) | Number of workers |
|---|---|
| $400 - 450$ | $2$ |
| $450 - 500$ | $6$ |
| $500 - 550$ | $12$ |
| $550 - 600$ | $18$ |
| $600 - 650$ | $24$ |
| $650 - 700$ | $13$ |
| $700 - 750$ | $5$ |
Use a graph paper to draw an ogive for the given data. Use a scale of $2 \; cm = $ ₹ $100$ on the X-axis and $2 \; cm = 20$ workers on the Y-axis.
From the ogive estimate
- the median wage of the workers;
- the inter-quartile range;
- the number of workers who earn more than ₹ $625$ daily.
| Wages (₹) (Class Interval) | Number of workers (frequency) | Cumulative Frequency |
|---|---|---|
| $400 - 450$ | $2$ | $2$ |
| $450 - 500$ | $6$ | $8$ |
| $500 - 550$ | $12$ | $20$ |
| $550 - 600$ | $18$ | $38$ |
| $600 - 650$ | $24$ | $62$ |
| $650 - 700$ | $13$ | $75$ |
| $700 - 750$ | $5$ | $80$ |
Total number of workers $= N = 80$
- Median wage of workers $= \left(\dfrac{N}{2}\right)^{th}$ term
$\begin{aligned} \text{i.e.} \; \text{Median wage} & = \left(\dfrac{80}{2}\right)^{th} \text{ term} \\\\ & = 40^{th} \text{ term} = 605 \end{aligned}$
i.e. $\;$ Median wage of workers $= $ ₹ $605$ - Lower quartile $= Q_1 = \left(\dfrac{N}{4}\right)^{th}$ term
i.e. $\;$ $Q_1 = \left(\dfrac{80}{4}\right)^{th}$ term $= 20^{th}$ term $= 550$
Upper quartile $= Q_3 = \left(\dfrac{3N}{4}\right)^{th}$ term
i.e. $\;$ $Q_3 = \left(\dfrac{3 \times 80}{4}\right)^{th}$ term $= 60^{th}$ term $= 640$
$\therefore \;$ Inter-quartile range $= Q_3 - Q_1 = 640 - 550 = 90$ - Number of workers who earn ₹ $625$ daily $= 50$
$\therefore \;$ Number of workers who earn more than ₹ $625$ daily $= 80 - 50 = 30$