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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
Find the mean of the following set of numbers:
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Attempt this question on graph paper.
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| No.of casualties | 6 | 10 | 15 | 13 | 24 | 8 | 7 |
(1) Construct the 'less than' Cumulative frequency curve for the above data. using 2 cm =10 years on one axis and 2 cm =10 casualties on the other.
(2)From your graph determine :
(a)the median
(b)the lower quartile
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 |
Find the median of the following:
11, 8, 15, 5, 9, 4, 19, 6, 18
Find the mean of x + 3, x + 5, x + 7, x + 9 and x + 11.
Find the median of the following sets of numbers.
25, 11, 15, 10, 17, 6, 5, 12.
A boy scored the 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, 16
What is his median marks?
The marks in a subject for 12 students are as follows:
31, 37, 35, 38, 42, 23, 17, 18, 35, 25, 35, 29
For the given data, find the median
The marks of 200 students in a test were recorded as follows:
| Marks % |
0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 | 90-100 |
| No. of students |
5 | 7 | 11 | 20 | 40 | 52 | 36 | 15 | 9 | 5 |
Using graph sheet draw ogive for the given data and use it to find the,
- median,
- number of students who obtained more than 65% marks
- number of students who did not pass, if the pass percentage was 35.
