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प्रश्न
The marks of 10 students of a class in an examination arranged in ascending order is as follows:
13, 35, 43, 46, x, x + 4, 55, 61, 71, 80
If the median marks is 48, find the value of x. Hence, find the mode of the given data.
उत्तर
Data in ascending order:
13, 35, 43, 46, x, x + 4, 55, 61, 71, 80
Median = 48
Number of observations = n = 10 ...(Even)
∴ Median = `((n/2)^"th" "term" + (n/2 + 1)^"th" "term")/2`
`=> 48 = ((10/2)^"th" "term" + (10/2 + 1)^"th" "term")/2`
`=> 48 = (5^"th" "term" + 6^"th" "term")/2`
`=> 48 = (x + x + 4)/2`
`=> 48 = (2x + 4)/2`
`=>` 48 = x + 2
`=>` x = 46
`=>` x + 4 = 46 + 4 = 50
Thus, the observations are 13, 35, 43, 46, 46, 50, 55, 61, 71, 80
Since 46 has highest frequency.
Hence, the mode of the data is 46.
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संबंधित प्रश्न
The marks of 200 students in a test were recorded as follows:
| Marks | No. of students |
| 10-19 | 7 |
| 20-29 | 11 |
| 30-39 | 20 |
| 40-49 | 46 |
| 50-59 | 57 |
| 60-69 | 37 |
| 70-79 | 15 |
| 80-89 | 7 |
Construct the cumulative frequency table. Drew the ogive and use it too find:
(1) the median and
(2) the number of student who score more than 35% marks.
Draw a histogram and hence estimate the mode for the following frequency distribution:
| Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
| Freq | 2 | 8 | 10 | 5 | 4 | 3 |
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
Draw a histogram for the following distribution and estimate the mode:
| I.Q. Score | 80-100 | 100-120 | 120-140 | 140-160 | 160-180 | 180-200 |
| No. of Students | 6 | 9 | 16 | 13 | 4 | 2 |
Find the median of all prime numbers between 20 and 50
Out of 10 students, who appeared in a test, three secured less than 30 marks and 3 secured more than 75 marks. The marks secured by the remaining 4 students are 35, 48, 66 and 40. Find the median score of the whole group.
The mean of a certain number of observations is 32. Find the resulting mean, if the observation is decreased by 20%.
If the mean of 8, 10, 7, x + 2 and 6 is 9, find the value of x.
Find the mean and the median of: 1.2, 1.9, 2.2, 2.6 and 2.9
The marks scored by the students in social test out of 20 marks are as follows: 12, 10, 8, 18, 14, 16. Find the mean and median?
