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The age of some students is given in years as 22, 23, 26, 28, 24, 29, 23, 27, 25 and 21. The median age (in years) of the students is:
24.5
23.5
24
25
24.5
Arrange in ascending order quickly by scanning smallest to largest. Since n=10 (even), the median is simply the average of the 5th and 6th terms.
Age of 10 students: 22, 23, 26, 28, 24, 29, 23, 27, 25, 21.
Median=2(2nтАЛ)th+(2nтАЛ+1)thтАЛ
Arrange in ascending order quickly by scanning smallest to largest. Since n=10 (even), the median is simply the average of the 5th and 6th terms.
Students often forget to arrange the data in ascending order before finding the middle terms, leading to incorrect values like 24 or 23.
Sort the data
Arrange the given ages in ascending order: 21, 22, 23, 23, 24, 25, 26, 27, 28, 29.
21,22,23,23,24,25,26,27,28,29
Identify n and middle positions
The number of observations n=10 (which is even). For an even number of observations, the median is the average of the 5th and 6th positions.
n=10,Pos=5,6
Calculate the median
Identify the 5th term (24) and 6th term (25) from the sorted list and calculate their mean.
Median=224+25тАЛ=24.5
A is correct because the average of the 5th and 6th terms, 24 and 25, results in a median of 24.5 years.
Always remember that for any set of data, the median is invariant to extreme outliers, unlike the Mean which is highly sensitive.
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