Advertisements
Advertisements
Question
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
2) The interquartile range.
3) The number of shooters who obtained a score of more than 85%.
Solution
| Scores | f | c.f. |
| 0 – 10 | 9 | 9 |
| 10 – 20 | 13 | 22 |
| 20 – 30 | 20 | 42 |
| 30 – 40 | 26 | 68 |
| 40 – 50 | 30 | 98 |
| 50 – 60 | 22 | 120 |
| 60 – 70 | 15 | 135 |
| 70 – 80 | 10 | 145 |
| 80 – 90 | 8 | 153 |
| 90 – 100 | 7 | 160 |
| n = 160 |
1) Median = `(n/2)^"th" term = (160/2)^"th"` term =80 term.
Through mark 80 on the y-axis, draw a horizontal line which meets the ogive drawn at point Q.
Through Q, draw a vertical line which meets the x-axis at the mark of 43.
⇒ Median = 43
2) Since the number of terms = 160
Lower quartile `(Q_1) = (160/4)^"th" "term" 120^"th" " term" = 60`
∴ Inter-quartile range = `Q_3 - Q_1` = 60 - 28 = 32
3) Since 85% scores = 85% of 100 = 85
Through mark for 85 on x-axis, draw a vertical line which meets the ogive drawn at point B.
Through the point B, draw a horizontal line which meets the y-axis at the mark of 150.
⇒ Number of shooters who obtained more than 85% score=160-150=10
APPEARS IN
RELATED QUESTIONS
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:
- a histrogram
- an ogive
- Use the information given in the adjoining histogram to construct a frequency table.
- Use this table to construct an ogive.
| Class mark | 12.5 | 17.5 | 22.5 | 27.5 | 32.5 | 37.5 | 42.5 |
| Frequency | 12 | 17 | 22 | 27 | 30 | 21 | 16 |
- From the distribution, given above, construct a frequency table.
- Use the table obtained in part (a) to draw : (i) a histogram, (ii) an ogive.
Use graph paper for this question.
The table given below shows the monthly wages of some factory workers.
- Using the table, calculate the cumulative frequencies of workers.
- Draw a cumulative frequency curve.
Use 2 cm = ₹ 500, starting the origin at ₹ 6500 on x-axis, and 2 cm = 10 workers on the y-axis.
| Wages (in ₹.) | 6500-7000 | 7000-7500 | 7500-8000 | 8000-8500 | 8500-9000 | 9000-9500 | 9500-10000 |
| No. of workers | 10 | 18 | 22 | 25 | 17 | 10 | 8 |
Income of 100 students of their parents is given as follows:
| Income (in thousand Rs.) |
No. of students (f) |
| 0 – 8 | 8 |
| 8 – 16 | 35 |
| 16 – 24 | 35 |
| 24 – 32 | 14 |
| 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:
- the median income.
- Calculate the income below which freeship will be awarded to students if their parents income is in the bottom 15%
- Mean income.
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.
The mark of 200 students in a test were recorded as follows:
| Marks % | No. of students |
| 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:
(i) The median
(ii) The number of students who scored more than 35% marks.
Use graph paper for this question.
The table given below shows the monthly wages of some factory workers.
(i) Using the table, calculate the cumulative frequency of workers.
(ii) Draw the cumulative frequency curve.
Use 2 cm = ₹500, starting the origin at ₹6,500 on X-axis, and 2 cm = 100 worker at they Y-axis.
(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 | - |
| 8500 - 9000 | 17 | - |
| 9000 - 9500 | 10 | - |
| 9500 - 10000 | 8 | - |
The marks obtained by 100 students in a Mathematics 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 | 3 | 7 | 12 | 17 | 23 | 14 | 9 | 6 | 5 | 4 |
Draw an ogive for the given distribution on a graph sheet.
Use a scale of 2 cm = 10 units on both axes.
Use the ogive to estimate the :
- median.
- lower quartile.
- number of students who obtained more than 85% marks in the test.
- number of students who did not pass in the test if the pass percentage was 35.
