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प्रश्न
If the mean of the following observations is 54, find the value of p.
| Class | 0 – 20 | 20 – 40 | 40 – 60 | 60 – 80 | 80 – 100 |
| Frequency | 7 | p | 10 | 9 | 13 |
उत्तर
| Class | Frequency (f) | Mid value (x) | fx |
| 0 – 20 | 7 | 10 | 70 |
| 20 – 40 | p | 30 | 30p |
| 40 – 60 | 10 | 50 | 500 |
| 60 – 80 | 9 | 70 | 630 |
| 80 – 100 | 13 | 90 | 1170 |
| Total | 39 + p | 2370 + 30p |
`barx = (sumfx)/(sumf) = (2370 + 30p)/(39 + p)` ...(i)
Here mean = 54 ...(ii)
From (i) and (ii)
`(2370 + 30p)/(39 + p) = 54`
`=>` 2370 + 30p = 2106 + 54p
`=>` 54p – 30p = 2370 – 2106
`=> p = 264/24 = 11`
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संबंधित प्रश्न
From the data given below, calculate the mean wage, correct to the nearest rupee.
| Category | A | B | C | D | E | F |
| Wages (Rs/day) | 50 | 60 | 70 | 80 | 90 | 100 |
| No. of workers | 2 | 4 | 8 | 12 | 10 | 6 |
- If the number of workers in each category is doubled, what would be the new mean wage?
- If the wages per day in each category are increased by 60%; what is the new mean wage?
- If the number of workers in each category is doubled and the wages per day per worker are reduced by 40%, what would be the new mean wage?
The following table gives the weekly wages of workers in a factory.
| Weekly wages (Rs) | No. of workers |
| 50 – 55 | 5 |
| 55 – 60 | 20 |
| 60 – 65 | 10 |
| 65 – 70 | 10 |
| 70 – 75 | 9 |
| 75 – 80 | 6 |
| 80 – 85 | 12 |
| 85 – 90 | 8 |
Calculate the mean by using:
Direct Method
Using a graph paper, draw an ogive for the following distribution which shows a record of the width in kilograms of 200 students.
| Weight | Frequency |
| 40 – 45 | 5 |
| 45 – 50 | 17 |
| 50 – 55 | 22 |
| 55 – 60 | 45 |
| 60 – 65 | 51 |
| 65 – 70 | 31 |
| 70 – 75 | 20 |
| 75 – 80 | 9 |
Use your ogive to estimate the following:
- The percentage of student weighting 55 kg or more
- The weight above which the heaviest 30% of the student fall
- The number of students who are
- underweight
- overweight, If 55.70 kg is considered as standard weight.
The monthly income of a group of 320 employees in a company is given below:
| Monthly income (thousands) | No. of employees |
| 6-7 | 20 |
| 7-8 | 45 |
| 8-9 | 65 |
| 9-10 | 95 |
| 10-11 | 60 |
| 11-12 | 30 |
| 12-13 | 5 |
Draw an ogive of the distribution on a graph paper taking 2 cm = Rs. 1000 on one axis and 2 cm = 50 employees on the other axis. From the graph detemine:
- the median wage.
- number of employee whose income is below Rs. 8,500.
- If salary of a senior employee is above Rs. 11,500, find the number of senior employee in the company.
- the upper quartile.
Find the mean (correct to one place of decimal) by using short-cut method.
|
x |
40 |
41 |
43 |
45 |
46 |
49 |
50 |
|
f |
14 |
28 |
38 |
50 |
40 |
20 |
10 |
Find the median of all prime numbers between 20 and 50
The mean of a certain number of observations is 32. Find the resulting mean, if the observation is, decreased by 7
Find the mean of: 7, 10, 4 and 17
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
The median of the data 24, 29, 34, 38, 35 and 30, is ___________
