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प्रश्न
Find the median of the following:
3x, x+5, x+7, x+9, x+11, x+13
उत्तर
3x, x+ 5, x+7, x+9, x+11, x+13
Arranging the given data in descending order:
x +13, x+ 11, x+9, x+7, x+5, 3x
The middle terms are x +9 and x+7 which are 3rd and 4th terms
median = `(x+9+x+ 7 )/2 = (2x+16 )/2 = x + 8`
Therefore, Median = x+8.
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संबंधित प्रश्न
The following are the marks obtained by 70 boys in a class test:
| Marks | No. of boys |
| 30 – 40 | 10 |
| 40 – 50 | 12 |
| 50 – 60 | 14 |
| 60 – 70 | 12 |
| 70 – 80 | 9 |
| 80 – 90 | 7 |
| 90 – 100 | 6 |
Calculate the mean by:
Step-deviation method
The mean of the following distribution is 62.8 and the sum of all the frequencies is 50. Find the missing frequencies f1 and f2.
| Class | 0 – 20 | 20 – 40 | 40 – 60 | 60 – 80 | 80 – 100 | 100 – 120 |
| Frequency | 5 | f1 | 10 | f2 | 7 | 8 |
Attempt this question on a graph paper. The table shows the distribution of marks gained by a group of 400 students in an examination.
|
Marks (Less than ) |
10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | 100 |
| No.of student | 5 | 10 | 30 | 60 | 105 | 180 | 270 | 355 | 390 | 400 |
Using scaie of 2cm to represent 10 marks and 2 cm to represent 50 student, plot these point and draw a smooth curve though the point
Estimate from the graph :
(1)the median marks
(2)the quartile marks.
Attempt this question on graph paper.
| Age (yrs ) | 5-15 | 15-25 | 25-35 | 35-45 | 45-55 | 55-65 | 65-75 |
| 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
The following table shows the frequency distribution of heights of 51 boys:
| Height (cm) | 120 | 121 | 122 | 123 | 124 |
| Frequency | 5 | 8 | 18 | 10 | 9 |
Find the mode of heights.
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.
Calculate the mean of the distribution, given below using the short cut method:
| Marks | 11 – 20 | 21 – 30 | 31 – 40 | 41 – 50 | 51 – 60 | 61 – 70 | 71 – 80 |
| No. of students | 2 | 6 | 10 | 12 | 9 | 7 | 4 |
If the mean of 11 , 14 , p , 26 , 10 , 12 , 18 , 6 is 15, find p.
Find the rnedian of the first 15 whole numbers .
The weekly sale of motor bikes in a showroom for the past 14 weeks given below. 10, 6, 8, 3, 5, 6, 4, 7, 12, 13, 16, 10, 4, 7. Find the median of the data.
