Advertisements
Advertisements
Question
Ten observations 6, 14, 15, 17, x + 1, 2x – 13, 30, 32, 34, 43 are written in an ascending order. The median of the data is 24. Find the value of x.
Solution
Given observations are 6, 14, 15, 17, x + 1, 2x – 13, 30, 32, 34, 43.
Here, total number of given observations, n = 10 ...(Even)
Since, n is even, so we use the formula for median,
Median = `((n/2)"th observation" + (n/2 + 1)"th observation")/2`
= `((10/2)"th observation" + (10/2 + 1)"th observation")/2` ...[Put n = 10]
= `(5"th observation" + 6"th observation")/2`
⇒ `24 = ((x + 1) + (2x - 13))/2` ...[Given]
⇒ 3x – 12 = 48
⇒ 3x = 60
⇒ x = 20
Hence, the value of x is 20.
APPEARS IN
RELATED QUESTIONS
If x is the mean of the ten natural numbers `x_1, x_2 , x_3+....... + x_10` show that (x1 -x) + (x2 - x) +.........+ (x10 - x)` = 0
If the mean of the following data is 15, find p.
| x: | 5 | 10 | 15 | 20 | 25 |
| f : | 6 | p | 6 | 10 | 5 |
Find the mean of the following distribution:
| x : | 10 | 12 | 20 | 25 | 35 |
| F : | 3 | 10 | 15 | 7 | 5 |
Find the median of the following data (1-8)
133, 73, 89, 108, 94, 1O4, 94, 85, 100, 120
The weights (in kg) of 15 students are: 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42,30. Find the median. If the weight 44 kg is replaced by 46 kg and 27 kg by 25 kg, find the new median.
Find the value of p, if the mean of the following distribution is 20.
| x: | 15 | 17 | 19 | 20+p | 23 |
| f: | 2 | 3 | 4 | 5p | 6 |
If the ratio of mode and median of a certain data is 6 : 5, then find the ratio of its mean and median.
The median of the following data : 0, 2, 2, 2, −3, 5, −1, 5, −3, 6, 6, 5, 6 is
A hockey player has scored following number of goals in 9 matches. 5, 4, 0, 2, 2, 4, 4, 3, 3.
Find the mean, median and mode of the data.
The mean marks (out of 100) of boys and girls in an examination are 70 and 73, respectively. If the mean marks of all the students in that examination is 71, find the ratio of the number of boys to the number of girls.
