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Question
The marks obtained by 120 students in a test are given below:
| Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 |
| No. of students |
5 | 9 | 16 | 22 | 26 | 18 | 11 | 6 | 4 | 3 |
Draw an ogive for the given distribution on a graph sheet.
Use a suitable scale for ogive to estimate the following:
(1) The median.
(2) The number of students who obtained more than 75% marks in the test.
(3) The number of students who did not pass the test if minimum marks required to pass is 40
Solution
| Marks | No. of Students | Cumulative Frequency |
| 0-10 | 5 | 5 |
| 10-20 | 9 | 14 |
| 20-30 | 16 | 30 |
| 30-40 | 22 | 52 |
| 40-50 | 26 | 78 |
| 50-60 | 18 | 96 |
| 60-70 | 11 | 107 |
| 70-80 | 6 | 113 |
| 80-90 | 4 | 117 |
| 90-100 | 3 | 120 |
`n = 120/2 = 60`
1) Through marks 60, draw a line segment parallel to x-axis which meets the curve at A. From A, draw a line perpendicular to x-axis meeting at B. Median = 43
2) Through marks 75, draw a line segment parallel to y-axis which meets the curve at D. From D, draw a line perpendicular to y-axis which meets y-axis at 110.
Number of students getting more than 75% = 120 - 110 = 10 students
3) Through marks 40, draw a line segment parallel to y-axis which meets the curve at C. From C, draw a line perpendicular to y-axis which meets y-axis at 52.
The number of students who did not pass = 52.
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The table shows the distribution of the scores obtained by 160 shooters in a shooting competition. Use a graph sheet and draw an ogive for the distribution. (Take 2 cm = 10 scores on the X-axis and 2 cm = 20 shooters on the Y-axis).
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Use your graph to estimate the following:
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3) The number of shooters who obtained a score of more than 85%.
Marks obtained by 200 students in an examination are given below:
| Marks | No. of students |
| 0 – 10 | 5 |
| 10 – 20 | 11 |
| 20 – 30 | 10 |
| 30 – 40 | 20 |
| 40 – 50 | 28 |
| 50 – 60 | 37 |
| 60 – 70 | 40 |
| 70 – 80 | 29 |
| 80 – 90 | 14 |
| 90 – 100 | 6 |
Draw an ogive for the given distribution taking 2 cm = 10 marks on one axis and 2 cm = 20 students on the other axis. Using the graph, determine:
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- If scoring 85 and more marks are considered as grade one, find the number of students who secured grade one in the examination.
Construct a frequency distribution table for the numbers given below, using the class intervals 21-30, 31-40, ... etc.
75, 65, 57, 26, 33, 44, 58, 67, 75, 78, 43, 41, 31, 21, 32, 40, 62, 54, 69, 48, 47, 51, 38, 39, 43, 61, 63, 68, 53, 56, 49, 59, 37, 40, 68, 23, 28, 36 and 47.
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| Wages (in ₹.) | 6500-7000 | 7000-7500 | 7500-8000 | 8000-8500 | 8500-9000 | 9000-9500 | 9500-10000 |
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| Marks | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 | 80 - 90 | 90 - 100 |
| Frequency | 5 | 11 | 10 | 20 | 28 | 37 | 40 | 29 | 14 | 6 |
Draw an ogive for the given distribution taking 2 cm = 10 marks on one axis and 2 cm = 20 students on the other axis. Using the graph, determine:
(i) The median marks
(ii) The number of students who failed if minimum marks required to pass is 40.
(iii) If scoring 85 and more marks is considered as grade one, find the number of students who secured grade one in the examination.
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| Marks | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 | 80 - 90 | 90 - 100 |
| No. of students | 5 | 10 | 14 | 21 | 25 | 34 | 36 | 27 | 16 | 12 |
Draw an ogive for the given distribution taking 2 cm = 10 makrs on one axis and 2 cm = 20 students on the other axis.
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| 10 - 19 | 7 |
| 20 - 29 | 11 |
| 30 - 39 | 20 |
| 40 - 49 | 46 |
| 50 - 59 | 57 |
| 60 - 69 | 37 |
| 70 - 79 | 15 |
| 80 - 89 | 7 |
Draw the cumulative frequency table.
Draw an ogive and use it to find:
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(ii) The number of students who scored more than 35% marks.
Use graph paper for this question.
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(iii) Use your graph to write down the median wages in ₹.
| Wages in ₹ (CLass) |
No. of workers (frequency) | Cumulative frequency f(x) |
| 6500 - 7000 | 10 | - |
| 7000 - 7500 | 18 | - |
| 7500 - 8000 | 22 | - |
| 8000 - 8500 | 25 | - |
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| 9000 - 9500 | 10 | - |
| 9500 - 10000 | 8 | - |
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| No. of Workers | 12 | 20 | 30 | 38 | 24 | 16 | 12 | 8 |
Using a graph paper, draw in Ogive for the above distribution.
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