Mathematics
Using a graph paper, draw an ogive for the distribution which shows the marks obtained on the General knowledge paper by 100 students.
| Marks | No. of students |
|---|---|
| 0 - 10 | 5 |
| 10 - 20 | 10 |
| 20 - 30 | 20 |
| 30 - 40 | 25 |
| 40 - 50 | 15 |
| 50 - 60 | 12 |
| 60 - 70 | 9 |
| 70 - 80 | 4 |
Use the ogive to estimate:
(i) the median
(ii) the number of students whose score is above 65.
Measures of Central Tendency
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Answer
Cumulative frequency distribution table :
| Marks | Number of students | Cumulative frequency |
|---|---|---|
| 0 - 10 | 5 | 5 |
| 10 - 20 | 10 | 15 (10 + 5) |
| 20 - 30 | 20 | 35 (15 + 20) |
| 30 - 40 | 25 | 60 (35 + 25) |
| 40 - 50 | 15 | 75 (60 + 15) |
| 50 - 60 | 12 | 87 (75 + 12) |
| 60 - 70 | 9 | 96 (87 + 9) |
| 70 - 80 | 4 | 100 (96 + 4) |
Here, n = 100, which is even.
(i) Steps of construction:
Take 1 cm along x-axis = 10 marks
Take 2 cm along y-axis = 20 students
Plot the point (0, 0) as ogive starts from x- axis representing lower limit of first class.
Plot the points (10, 5), (20, 15), (30, 35), (40, 60), (50, 75), (60, 87), (70, 96), (80, 100).
Joint the points by a free hand curve.
To find the median :
Let A be the point on y-axis representing frequency = = 50.
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 points M represents 36.
Hence, the median is 36.
(ii) Total marks = 100.
Let E be the point on x-axis representing marks = 65.
Through E draw a vertical line to meet the ogive at B. Through B, draw a horizontal line to meet the y-axis at C. The ordinate of the point C represents 93.
Hence, 93 students score less than or equal to 65, so, students scoring more than 65 = 100 - 93 = 7.
Hence, the number of students who scored more than 65 marks is 7.
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