Mathematics
Using the data given below construct the cumulative frequency table and draw the ogive. From the ogive, determine the median.
| Marks | No. of students |
|---|---|
| 0 - 10 | 3 |
| 10 - 20 | 8 |
| 20 - 30 | 12 |
| 30 - 40 | 14 |
| 40 - 50 | 10 |
| 50 - 60 | 6 |
| 60 - 70 | 5 |
| 70 - 80 | 2 |
Measures of Central Tendency
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Answer
- The cumulative frequency table for the given continuous distribution is :
| Marks | No. of students | Cumulative frequency |
|---|---|---|
| 0 - 10 | 3 | 3 |
| 10 - 20 | 8 | 11 |
| 20 - 30 | 12 | 23 |
| 30 - 40 | 14 | 37 |
| 40 - 50 | 10 | 47 |
| 50 - 60 | 6 | 53 |
| 60 - 70 | 5 | 58 |
| 70 - 80 | 2 | 60 |
Take 1 cm along x-axis = 10 marks
Take 1 cm along y-axis = 10 (students)
Plot the points (10, 3), (20, 11), (30, 23), (40, 37), (50, 47), (60, 53), (70, 58) and (80, 60) representing upper class limits and the respective cumulative frequencies.
Also plot the point representing lower limit of the first class i.e. 0 - 10.
- Join these points by a freehand drawing.
The required ogive is shown in figure above.
Here, n (no. of students) = 60.
To find the median :
Let A be the point on y-axis representing frequency = = 30.
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 35 marks.
Hence, the required median = 35 marks.
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