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प्रश्न
Using step-deviation method, calculate the mean marks of the following distribution.
| C.I. | 50 – 55 | 55 – 60 | 60 – 65 | 65 – 70 | 70 – 75 | 75 – 80 | 80 – 85 | 85 – 90 |
| Frequency | 5 | 20 | 10 | 10 | 9 | 6 | 12 | 8 |
उत्तर
Let the assumed mean A = 72.5
|
C.I. |
fi |
Mid-value |
A = 72.5 `bb(t = (x - A)/i)` |
fiti |
| 50 – 55 | 5 | 52.5 | –4 | –20 |
| 55 – 60 | 20 | 57.5 | –3 | –60 |
| 60 – 65 | 10 | 62.5 | –2 | –20 |
| 65 – 70 | 10 | 67.5 | –1 | –10 |
| 70 – 75 | 9 | 72.5 | 0 | 0 |
| 75 – 80 | 6 | 77.5 | 1 | 6 |
| 80 – 85 | 12 | 82.5 | 2 | 24 |
| 85 – 90 | 8 | 87.5 | 3 | 24 |
| Total | 80 | –56 |
Mean = `A + (f_it_i)/n xx i`
= `72.5 + (-56/80) xx 5`
= 72.5 – 0.7 × 5
= 72.5 – 3.5
= 69
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संबंधित प्रश्न
The following are the marks obtained by 70 boys in a class test:
| Marks | No. of boys |
| 30 – 40 | 10 |
| 40 – 50 | 12 |
| 50 – 60 | 14 |
| 60 – 70 | 12 |
| 70 – 80 | 9 |
| 80 – 90 | 7 |
| 90 – 100 | 6 |
Calculate the mean by:
Short-cut method
The marks of 20 students in a test were as follows:
2, 6, 8, 9, 10, 11, 11, 12, 13, 13, 14, 14, 15, 15, 15, 16, 16, 18, 19 and 20.
Calculate:
- the mean
- the median
- the mode
The distribution, given below, shows the marks obtained by 25 students in an aptitude test. Find the mean, median and mode of the distribution.
| Marks obtained | 5 | 6 | 7 | 8 | 9 | 10 |
| No. of students | 3 | 9 | 6 | 4 | 2 | 1 |
Find the arithmetic mean (correct to the nearest whole number) by using step-deviation method.
| x | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | 45 | 50 |
| f | 20 | 43 | 75 | 67 | 72 | 45 | 39 | 9 | 8 | 6 |
In a case of 40 students, marks obtained by the students in a class test (out of 10) are given below:
| Marks | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| Number of students | 1 | 2 | 3 | 3 | 6 | 10 | 5 | 4 | 3 | 3 |
Calculate the following for the given distribution:
(i) Median
(ii) Mode
Find the mode of the following frequency distribution:
| Pocket money per week in Rs | 25 | 50 | 75 | 100 | 125 | 150 |
| No. of students | 4 | 7 | 13 | 18 | 6 | 2 |
Draw a histogram for the following distribution and estimate the mode:
| I.Q. Score | 80-100 | 100-120 | 120-140 | 140-160 | 160-180 | 180-200 |
| No. of Students | 6 | 9 | 16 | 13 | 4 | 2 |
The marks of 200 students in a test is given below :
| Marks% | 10-19 | 20-29 | 30-39 | 40-49 | 50-59 | 60-69 | 70-79 | 80-89 |
| No. of Students | 7 | 11 | 20 | 46 | 57 | 37 | 15 | 7 |
Draw an ogive and find
(i) the median
(ii) the number of students who scored more than 35% marks
Find the median of the following sets of numbers.
25, 11, 15, 10, 17, 6, 5, 12.
The mean of five positive integers is twice their median. If four of the integers are 3, 4, 6, 9 and median is 6, then find the fifth integer
