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प्रश्न
Calculate the mean of the distribution given below using the shortcut method.
| Marks | 11-20 | 21-30 | 31-40 | 41-50 | 51-60 | 61-70 | 71-80 |
| No. of students | 2 | 6 | 10 | 12 | 9 | 7 | 4 |
उत्तर
Let A be the assumed mean and d be the deviation of x from the assumed mean.
Let A = 45.5.
d = x – A
| Marks (C.I.) | No. of students (Frequency f) |
Mid-point of C.I. (x) |
d = x – A | f × d |
| 11-20 | 2 | 15.5 | -30 | -60 |
| 21-30 | 6 | 25.5 | -20 | -120 |
| 31-40 | 10 | 35.5 | -10 | -100 |
| 41-50 | 12 | 45.5 | 0 | 0 |
| 51-60 | 9 | 55.5 | 10 | 90 |
| 61-70 | 7 | 65.5 | 20 | 140 |
| 71-80 | 4 | 75.5 | 30 | 120 |
| `sumfd = 70` |
Mean = `A + (sumfd)/(sum f)`
`=> Mean = 45.5 + 70/50`
`=> Mean = 45.5 + 1.4`
`:. Mean = 45.9`
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संबंधित प्रश्न
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
The data on the number of patients attending a hospital in a month are given below. Find the average (mean) number of patients attending the hospital in a month by using the shortcut method. Take the assumed mean as 45. Give your answer correct to 2 decimal places.
| Number of patients | 10 - 20 | 20 - 30 | 30 - 40 | 40 - 50 | 50 - 60 | 60 - 70 |
| Number of Days | 5 | 2 | 7 | 9 | 2 | 5 |
Find the mean of the following frequency distribution :
| class | 0-6 | 6-12 | 12-18 | 18-24 | 24-30 |
| Frequency | 7 | 5 | 10 | 12 | 6 |
Find the mean of the following frequency distribution by the short cut method :
| Class | 1-10 | 11-20 | 21-30 | 31-40 | 41-50 | 51-60 | 61-70 |
| Frequency | 7 | 10 | 14 | 17 | 15 | 11 | 6 |
Find the mode of the following:
3, 4, 5, 7, 6, 3, 5, 4, 3, 5, 6, 4, 7, 5, 4, 5, 4, 3, 4, 5, 7, 6, 5, 6, 6, 7
Find the mean of: 5, 2.4, 6.2, 8.9, 4.1 and 3.4
If the mean of x, x + 2, x + 4, x + 6 and x + 8 is 13, find the value of x. Sum of data.
3, 8, 10, x, 14, 16, 18, 20 are in the ascending order and their median is 13. Calculate the numerical value of x.
A boy scored the following marks in various class tests during a term, each test being marked out of 20.
15, 17, 16, 7, 10, 12, 14, 16, 19, 12, 16
What is his median marks?
The marks of 200 students in a test were recorded as follows:
| 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 | 7 | 11 | 20 | 40 | 52 | 36 | 15 | 9 | 5 |
Using graph sheet draw ogive for the given data and use it to find the,
- median,
- number of students who obtained more than 65% marks
- number of students who did not pass, if the pass percentage was 35.
