Mathematics
The daily wages of 80 workers in a project are given below :
| Wages (in ₹) | No. 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 above distribution. (Use a scale of 2 cm = ₹ 50 on x-axis and 2 cm = 10 workers on y-axis). Use your ogive to estimate :
(i) the median wage of the workers.
(ii) the lower quartile wage of the workers.
(iii) the number of workers who earn more than ₹625 daily.
Measures of Central Tendency
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Answer
- The cumulative frequency table for the given continuous distribution is :
| Wages (in ₹) | No. of workers | 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 |
Take 2 cm along x-axis = 50 rupees
Take 1 cm along y-axis = 10 workers
Since, scale on x-axis starts at 400, a kink is shown near the origin on x-axis to indicate that the graph is drawn to scale beginning at 400.
Plot the points (450, 2), (500, 8), (550, 20), (600, 38), (650, 62), (700, 75) and (750, 80) representing upper class limits and the respective cumulative frequencies.
Also plot the point representing lower limit of the first class i.e. 400 - 450.Join these points by a freehand drawing.
The required ogive is shown in figure above.
(i) Here, n (no. of students) = 80.
To find the median :
Let A be the point on y-axis representing frequency = = 40.
Through A draw a horizontal line to meet the ogive at P. Through P, draw a vertical line to meet the x-axis at M. The abscissa of the point M represents 604.
Hence, the required median wage = ₹604.
(ii) To find lower quartile :
Let B be the point on y-axis representing frequency = = 20
Through B, draw a horizontal line to meet the ogive at Q. Through Q, draw a vertical line to meet the x-axis at N. The abscissa of the point N represents 550.
Hence, lower quartile wage = ₹550.
(iii) Let T be the point on x-axis representing wage = ₹625.
Through T, draw a vertical line to meet the ogive at S. Through S, draw a horizontal line to meet the y-axis at C. The ordinate of the point C represents 51.
Workers who earn less than ₹625 = 51.
So, workers earning more than ₹625 = Total workers - workers who earn less than ₹625 = 80 - 51 = 29.
Hence, there are 29 workers earning more more than ₹625 daily.
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