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प्रश्न
In 10 numbers, arranged in increasing order, the 7th number is increased by 8, how much will the median be changed?
उत्तर
For any given set of data, the median is the value of its middle term.
Here, total observations = n = 10 (even)
If n is even, we have
Median =`1/2 [ "value of" (n/2)^"th" "term" + "value of" (n/2 +1)^"th" "term" ]`
Thus, for n = 10, we have
Median =`1/2 [ "value of"(10/2)^"th" "term" + "value of" (( 10 )/(2) + 1)^"th" "term" ]`
=`1/2 [ "value of "5^"th" "term" + "value of " 6^"th" "term" ]`
Hence, if the 7th number is diminished, decreasing by 8, there is no change in the median value.
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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 mean of the following distribution is 52 and the frequency of class interval 30-40 is ‘f’. Find ‘f’.
| Class Interval | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 |
| Frequency | 5 | 3 | f | 7 | 2 | 6 | 13 |
The mean of the number 6, ‘y’, 7, ‘x’ and 14 is 8. Express ‘y’ in terms of ‘x’.
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.
The marks obtained by 120 students in a mathematics test is given below:
| Marks | No. of students |
| 0 – 10 | 5 |
| 10 – 20 | 9 |
| 20 – 30 | 16 |
| 30 – 40 | 22 |
| 40 – 50 | 26 |
| 50 – 60 | 18 |
| 60 – 70 | 11 |
| 70 – 80 | 6 |
| 80 – 90 | 4 |
| 90 – 100 | 3 |
Draw an ogive for the given distributions on a graph sheet. Use a suitable scale for your ogive. Use your ogive to estimate:
- the median
- the number of student who obtained more than 75% in test.
- the number of students who did not pass in the test if the pass percentage was 40.
- the lower quartile.
The pocket expenses (per day) of Anuj, during a certain week, from Monday to Saturday were ₹85.40, ₹88.00, ₹86.50, ₹84.75, ₹82.60 and ₹87.25. Find the mean pocket expenses per day.
Find the mean of the first six multiples of 5.
Find the mean of: 7, 5, 0, 3, 0, 6, 0, 9, 1 and 4
Find the mean of: 2.1, 4.5, 5.2, 7.1 and 9.3
Find the median of the following sets of numbers.
15, 8, 14, 20, 13, 12, 16
