Mathematics
100 pupils in a school have heights as tabulated below :
| Height (in cm) | No. of pupils |
|---|---|
| 121 - 130 | 12 |
| 131 - 140 | 16 |
| 141 - 150 | 30 |
| 151 - 160 | 20 |
| 161 - 170 | 14 |
| 171 - 180 | 8 |
Draw the ogive for the above data and from it determine the median (use graph paper).
Measures of Central Tendency
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Answer
Converting the discontinuous data into continuous data.
Adjustment factor = (Lower limt of one class - Upper limit of previous class) / 2
- We construct the table as under :
| Classes before adjustment | Classes after adjustment | No. of pupils | Cumulative frequency |
|---|---|---|---|
| 121 - 130 | 120.5 - 130.5 | 12 | 12 |
| 131 - 140 | 130.5 - 140.5 | 16 | 28 |
| 141 - 150 | 140.5 - 150.5 | 30 | 58 |
| 151 - 160 | 150.5 - 160.5 | 20 | 78 |
| 161 - 170 | 160.5 - 170.5 | 14 | 92 |
| 171 - 180 | 170.5 - 180.5 | 8 | 100 |
Take 1 cm along x-axis = 10 cm
Take 1 cm along y-axis = 10 (people)
Since, scale on x-axis starts at 120.5, a kink is shown near the origin on x-axis to indicate that the graph is drawn to scale beginning at 120.5
Plot the points (130.5, 12), (140.5, 28), (150.5, 58), (160.5, 78), (170.5, 92) and (180.5, 100) representing upper class limits and the respective cumulative frequencies.
Also plot the point representing lower limit of the first class i.e. 120.5 - 130.5.Join these points by a freehand drawing.
The required ogive is shown in figure above.
Here, n (no. of students) = 100.
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 point M represents height = 147.5 cm.
Hence, the median height = 147.5 cm.
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Related Questions
The following distribution represents the height of 160 students of a school.
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(i) The median height.
(ii) The inter quartile range.
(iii) The number of students whose height is above 172 cm.
The marks obtained by 120 students in a Mathematics test are given below:
Marks No. of students 0 - 10 5 10 - 20 9 20 - 30 16 30 - 40 22 40 - 50 26 50 - 60 18 60 - 70 11 70 - 80 6 80 - 90 4 90 - 100 3 Draw an ogive for the given distribution on a graph sheet. Use a suitable scale for ogive to estimate the following :
(i) the median
(ii) the number of students who obtained more than 75% marks in the test.
(iii) the number of students who did not pass in the test if the pass percentage was 40.
Use graph paper for this question.
A survey regarding height (in cm) of 60 boys belonging to class 10 of a school was conducted. The following data was recorded :
Height (in cm) No. of boys 135 - 140 4 140 - 145 8 145 - 150 20 150 - 155 14 155 - 160 7 160 - 165 6 165 - 170 1 Taking 2 cm = height of 10 cm on one axis and 2 cm = 10 boys along the other axis, draw an ogive of the above distribution. Use the graph to estimate the following :
(i) median
(ii) lower quartile
(iii) if above 158 is considered as the tall boy of the class, find the number of boys in the class who are tall.
The marks obtained by 100 students in a Mathematics test are given below :
Marks No. of students 0 - 10 3 10 - 20 7 20 - 30 12 30 - 40 17 40 - 50 23 50 - 60 14 60 - 70 9 70 - 80 6 80 - 90 5 90 - 100 4 Draw an ogive on a graph sheet and from it determine the :
(i) median
(ii) lower quartile
(iii) number of students who obtained more than 85% marks in the test
(iv) number of students who did not pass in the test if the pass percentage was 35.