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The median of observations 11,12,14,18,x 2,x 4,30,32,35,41 arranged in ascending order is 24. What is value of x?
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The median of observations 11,12,14,18,x 2,x 4,30,32,35,41 arranged in...
Problem Statement:
Find the value of x in the given observation 11, 12, 14, 18, x2, x4, 30, 32, 35, 41 arranged in ascending order, if the median of the observations is 24.
Solution:
Given observations are:
11, 12, 14, 18, x2, x4, 30, 32, 35, 41
Arranging them in ascending order:
11, 12, 14, 18, x2, x4, 30, 32, 35, 41
Median of the given observations is 24.
Let's find out the position of median:
Since there are 10 observations, the position of the median will be (10+1)/2 = 5.5
Therefore, the median lies between the 5th and 6th observation when arranged in ascending order.
From the given observations, we can see that:
11, 12, 14, 18, x2, x4, 30, 32, 35, 41
5th observation = x2
6th observation = x4
Since the median is 24, we can say that:
x2 + x4 = 48
Dividing both sides by 2, we get:
x2 = 24 - x4
Substituting this value of x2 in the first equation, we get:
(24 - x4) + x4 = 48
24 + x4 = 48
x4 = 24
Therefore, x2 = 24 - x4 = 24 - 24 = 0
So, the value of x is:
x = x2 + x4 = 0 + 24 = 24
Conclusion:
The value of x in the given observation is 24.
Community Answer
The median of observations 11,12,14,18,x 2,x 4,30,32,35,41 arranged in...
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The median of observations 11,12,14,18,x 2,x 4,30,32,35,41 arranged in ascending order is 24. What is value of x?
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