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प्रश्न
The following observations have been arranged in ascending order. If the median of the data is 78, find the value of x.
44, 47, 63, 65, x + 13, 87, 93, 99, 110.
उत्तर
Consider the given data :
44, 47, 63, 65, x + 13, 87, 93, 99, 110
Here the number of observations is 9, which is odd.
Thus, the median of the given data is `([n + 1 ]/2)^"th"` observation.
From the given data, `([9 + 1 ]/ 2 = 5)^"th"` observation is x + 13
Also, given that the median is 78.
x + 13 = 78
⇒ x = 78 - 13
⇒ x = 65
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संबंधित प्रश्न
1) Using step–deviation method, calculate the mean marks of the following distribution.
2) State the modal class.
| Class Interval | 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 |
The ages of 40 students are given in the following table :
| Age (in years) | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
| Frequency | 2 | 4 | 6 | 9 | 8 | 7 | 4 |
Find the arithmetic mean.
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?
A boy scored 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 and 16
What are his total marks?
The following table given the weekly of workers in a factory:
| Weekly wages (in 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 |
Calcculate: (1)the mean, (2) the model class, (3) th number of workers getting weekly qages below Rs. 80 and (4) the number of workers getting Rs. 65 or more but less than Rs.85 as weekly wages.
Find the mean of the following frequency distribution :
| Class | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 |
| Frequency | 8 | 6 | 12 | 11 | 13 |
Find the mode of the following:
20, 20, 30, 30, 30, 30, 35, 40, 40, 45, 45, 45, 50, 55, 60, 60, 60 ,65, 70, 70, 70
Draw a histogram for the following distribution and estimate the mode:
| Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
| No. of students | 3 | 7 | 15 | 24 | 16 | 8 | 5 | 2 |
Find the mean of: 3, 1, 5, 4, 4 and 7
Find the median of 26, 33, 41, 18, 30, 22, 36, 45 and 24
