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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
If the mean of the following distribution is 24, find the value of 'a '.
| Marks | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 |
| Number of students |
7 | a | 8 | 10 | 5 |
From the following cumulative frequency table, draw ogive and then use it to find:
- Median
- Lower quartile
- Upper quartile
| Marks (less than) | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |
| Cumulative frequency | 5 | 24 | 37 | 40 | 42 | 48 | 70 | 77 | 79 | 80 |
Draw an ogive for the data given below and from the graph determine:
- the median marks
- the number of students who obtained more than 75% marks
| Marks | No. of students |
| 0 – 9 | 5 |
| 10 – 19 | 9 |
| 20 – 29 | 16 |
| 30 – 39 | 22 |
| 40 – 49 | 26 |
| 50 – 59 | 18 |
| 60 – 69 | 11 |
| 70 – 79 | 6 |
| 80 – 89 | 4 |
| 90 – 99 | 3 |
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
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2, 3, 5, 9, x + 1, x + 3, 14, 16, 19, 20
If the median of the data is 11, find the value of x.
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