Mathematics
The weight of 50 workers is given below :
| Weight (in kg) | No. of workers |
|---|---|
| 50 - 60 | 4 |
| 60 - 70 | 7 |
| 70 - 80 | 11 |
| 80 - 90 | 14 |
| 90 - 100 | 6 |
| 100 - 110 | 5 |
| 110 - 120 | 3 |
Draw an ogive of the given distribution using a graph sheet. Take 2 cm = 10 kg on one axis and 2 cm = 5 workers along the other axis. Use a graph to estimate the following :
(i) the upper and lower quartiles.
(ii) if weighing 95 kg and above is considered overweight find the number of workers who are overweight.
Measures of Central Tendency
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Answer
- The cumulative frequency table for the given continuous distribution is :
| Weight (in kg) | No. of workers | Cumulative frequency |
|---|---|---|
| 50 - 60 | 4 | 4 |
| 60 - 70 | 7 | 11 |
| 70 - 80 | 11 | 22 |
| 80 - 90 | 14 | 36 |
| 90 - 100 | 6 | 42 |
| 100 - 110 | 5 | 47 |
| 110 - 120 | 3 | 50 |
Take 1 cm along x-axis = 10 kg
Take 1 cm along y-axis = 5 (workers)
Since, scale on x-axis starts at 50, a kink is shown near the origin on x-axis to indicate that the graph is drawn to scale beginning at 50.
Plot the points (60, 4), (70, 11), (80, 22), (90, 36), (100, 42), (110, 47) and (120, 50) representing upper class limits and the respective cumulative frequencies.
Also plot the point representing lower limit of the first class i.e. 50 - 60.
- Join these points by a freehand drawing.
The required ogive is shown in figure above.
(i) To find lower quartile :
Let A be the point on y-axis representing frequency = = 12.5
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 71 kg.
To find upper quartile :
Let B be the point on y-axis representing frequency = = 37.5
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 93 kg.
Hence, lower quartile = 71 kg and upper quartile = 93 kg.
(ii) Let O be the point on x-axis representing 95 kg. Through O draw a vertical line to meet the ogive R. Through R, draw a horizontal line to meet the y-axis at point C. The ordinate of the point C represents 39.
So, the number of people whose weight is less than 95 kg = 39. So, overweight people = 50 - 39 = 11 kg.
Hence, the number of workers who are overweight are 11.
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