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The following observations are arranged in ascending order. 29,32,38,50,x,x+2,72,78,84,95 If the median is 63, then the value of x is:
50
31
63
62
62
Since the sequence is even-numbered (10 terms), the median is the average of the 5th and 6th terms. Solve for x by averaging x and (x+2) = 63.
Observations: 29, 32, 38, 50, x, x + 2, 72, 78, 84, 95. Number of observations n = 10. Median = 63.
Median=2Value┬аof┬а(2nтАЛ)th┬аterm+Value┬аof┬а(2nтАЛ+1)th┬аtermтАЛ
Since the sequence is even-numbered (10 terms), the median is the average of the 5th and 6th terms. Solve for x by averaging x and (x+2) = 63.
Students often pick the middle value from an odd number formula or incorrectly index the (n/2)th term for even sets.
Identify terms
With n=10 observations, the median is the arithmetic mean of the 5th and 6th observations.
5th=x,6th=x+2
Apply median formula
Set the average of the 5th and 6th terms equal to the given median of 63.
2x+(x+2)тАЛ=63
Solve for x
Simplify the equation: (2x+2)/2=63, which leads to x+1=63.
x=63тИТ1=62
D is correct because solving the equation 2x+x+2тАЛ=63 gives x=62.
This is a fundamental statistics problem. Always check if the dataset is already ordered before applying the median formula.
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