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प्रश्न
The following distribution shows the daily pocket allowance given to the children of a multistorey building. The average pocket allowance is Rs 18.00. Find out the missing frequency.
| Class interval | 11 - 13 | 13 - 15 | 15 - 17 | 17 - 19 | 19 - 21 | 21 - 23 | 23 - 25 |
| Frequency | 7 | 6 | 9 | 13 | - | 5 | 4 |
उत्तर
Given mean = 18, let missing frequency be 'x'.
| Class interval | Mid value(x1) | Frequency(f1) | f1x1 |
| 11 - 13 | 12 | 7 | 84 |
| 13 - 15 | 14 | 6 | 84 |
| 15 - 17 | 16 | 9 | 144 |
| 17 - 19 | 18 | 13 | 234 |
| 19 - 21 | 20 | x | 20x |
| 21 - 23 | 22 | 5 | 110 |
| 23 - 25 | 24 | 4 | 96 |
| N = 44 + x | 752 + 20x |
Mean `=(sumf_1x_1)/N`
`18=(752+20x)/(44+x)`
(44 + x)18 = 752 + 20x
792 + 18x = 752 + 20x
20x - 18x = 792 - 752
2x = 40
x = 40/2 = 20
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संबंधित प्रश्न
Find the missing frequencies in the following frequency distribution if it is known that the mean of the distribution is 50.
| x | 10 | 30 | 50 | 70 | 90 | |
| f | 17 | f1 | 32 | f2 | 19 | Total 120 |
The arithmetic mean of the following data is 14. Find the value of k
| x1 | 5 | 10 | 15 | 20 | 25 |
| f1 | 7 | k | 8 | 4 | 5 |
In the first proof reading of a book containing 300 pages the following distribution of misprints was obtained:
| No. of misprints per page (x) | 0 | 1 | 2 | 3 | 4 | 5 |
| No. of pages (f) | 154 | 95 | 36 | 9 | 5 | 1 |
Find the average number of misprints per page.
Find the mean of each of the following frequency distributions: (5 - 14)
| Class interval | 0 - 6 | 6 - 12 | 12 - 18 | 18 - 24 | 24 - 30 |
| Frequency | 6 | 8 | 10 | 9 | 7 |
Find the mean of each of the following frequency distributions
| Class interval | 0 - 8 | 8 - 16 | 16 - 24 | 24 - 32 | 32 - 40 |
| Frequency | 6 | 7 | 10 | 8 | 9 |
Find the mean using direct method:
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
| Frequency | 7 | 5 | 6 | 12 | 8 | 2 |
The daily expenditure of 100 families are given below. Calculate `f_1` and `f_2` if the mean daily expenditure is ₹ 188.
|
Expenditure (in Rs) |
140-160 | 160-180 | 180-200 | 200-220 | 220-240 |
|
Number of families |
5 | 25 | `f_1` | `f_2` | 5 |
In the formula
The daily income of a sample of 50 employees are tabulated as follows:
| Income (in Rs) |
1 – 200 | 201 – 400 | 401 – 600 | 601 – 800 |
| Number of employees |
14 | 15 | 14 | 7 |
Find the mean daily income of employees.
The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table:
| Length (in mm) | Number of leaves |
| 118−126 | 3 |
| 127–135 | 5 |
| 136−144 | 9 |
| 145–153 | 12 |
| 154–162 | 5 |
| 163–171 | 4 |
| 172–180 | 2 |
Find the mean length of the leaves.
