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Question
Marks obtained by 200 students in an examination are given below:
| 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.
Solution
On graph
| Marks | 0 - 10 | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 | 70 - 80 | 80 - 90 | 90 - 100 |
| f | 5 | 11 | 10 | 20 | 28 | 37 | 40 | 29 | 14 | 6 |
| c.f. | 5 | 16 | 26 | 46 | 74 | 111 | 151 | 180 | 194 | 200 |
(i) Median = `("n"/2)^"th" "obv" = (200/2)^"th" "obv"`.
= 100th obv.
= 57
(ii) No. of students who failed = 46
(iii) No. of students who secured grade one = 200 - 188 = 12.
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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).
| Scores | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 |
| No. of shooters |
9 | 13 | 20 | 26 | 30 | 22 | 15 | 10 | 8 | 7 |
Use your graph to estimate the following:
1) The median
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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:
- The median marks.
- The number of students who failed if minimum marks required to pass is 40.
- 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.
Use the table obtained to draw:
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- Use this table to construct an ogive.
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| Frequency | 12 | 17 | 22 | 27 | 30 | 21 | 16 |
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Income of 100 students of their parents is given as follows:
| Income (in thousand Rs.) |
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| 0 – 8 | 8 |
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| 32 – 40 | 8 |
Draw an ogive for the given distribution on a graph sheet. Use a suitable scale for your exercise. Use your ogive to estimate:
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Attempt this question on graph paper. Marks obtained by 200 students in examination 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 | 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.
From the graph find:
(i) the median
(ii) the upper quartile
(iii) number of student scoring above 65 marks.
(iv) If to students qualify for merit scholarship, find the minimum marks required to qualify.
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 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.
