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Find the median of the following data: 12, 45, 23, 12, 56, 89, 34, 12, 67, 45.
34
39.5
45
23
39.5
Arrange only the first few and last few numbers in ascending order to identify the middle values quickly; since n=10 is even, locate the 5th and 6th terms.
A set of 10 observations: 12, 45, 23, 12, 56, 89, 34, 12, 67, 45.
Median=2(2nтАЛ)th┬аterm+(2nтАЛ+1)th┬аtermтАЛ
Arrange only the first few and last few numbers in ascending order to identify the middle values quickly; since n=10 is even, locate the 5th and 6th terms.
Students often forget to arrange the data in ascending order before finding the middle term, leading to incorrect calculations.
Sort the data
Arrange the 10 observations in non-decreasing order: 12, 12, 12, 23, 34, 45, 45, 56, 67, 89.
12,12,12,23,34,45,45,56,67,89
Identify middle terms
Since the total number of observations n=10 (even), the median is the average of the 5th and 6th terms.
5th=34,6th=45
Calculate the average
Applying the formula for even n: Median=(34+45)/2=79/2.
234+45тАЛ=39.5
B is correct because the average of the 5th and 6th terms (34 and 45) is 39.5.
For large datasets, use the cumulative frequency distribution to find the median position, which is a key concept in Grouped Frequency Distributions.
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