Mathematics
The median of the observations 11, 12, 14, (x - 2), (x + 4), (x + 9), 32, 38, 47 are arranged in ascending order is 24. Find the value of x and hence find the mean.
Measures of Central Tendency
1 Like
Answer
No. of observations (n) = 9.
Here, n = 9, which is odd.
Median = th term
= = 5th term
= x + 4.
Given, median = 24
⇒ x + 4 = 24
⇒ x = 20.
Observations = 11, 12, 14, (x - 2), (x + 4), (x + 9), 32, 38, 47
= 11, 12, 14, 18, 24, 29, 32, 38, 47.
Sum of observations = 11 + 12 + 14 + 18 + 24 + 29 + 32 + 38 + 47
= 225.
Mean = = 25.
Hence, x = 20 and mean = 25.
Answered By
3 Likes
Related Questions
The monthly income of a group of 320 employees in a company is given below :
Monthly income No. of employees 6 - 7 20 7 - 8 45 8 - 9 65 9 - 10 95 10 - 11 60 11 - 12 30 12 - 13 5 Draw an ogive of the given distribution on a graph sheet taking 2 cm = ₹ 1000 on one axis and 2 cm = 50 employees on the other axis. From the graph determine :
(i) the median wage.
(ii) the number of employees whose income is below ₹ 8500.
(iii) if the salary of a senior employee is above ₹ 11500, find the number of senior employees in the company.
(iv) the upper quartile.
The numbers 6, 8, 10, 12, 13 and x are arranged in an ascending order. If the mean of the observations is equal to the median, find the value of x.
The mean of numbers 45, 52, 60, x, 69, 70, 26, 81 and 94 is 68. Find the value of x. Hence, estimate the median for the resulting data.
The distribution given below, shows the marks obtained by 25 students in an aptitude test. Find the mean, median and mode of the distribution.
Marks obtained No. of students 5 3 6 9 7 6 8 4 9 2 10 1