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Find the median of the following data: 12, 45, 23, 12, 56, 89, 34, 12, 67, 90.
34
39.5
45
23
39.5
Count the total terms first; since n=10 (even), immediately identify the 5th and 6th terms from the ordered list to find the average.
Data set: 12, 45, 23, 12, 56, 89, 34, 12, 67, 90. Total number of observations (n) = 10.
Median=2(2nтАЛ)thterm+(2nтАЛ+1)thtermтАЛ
Count the total terms first; since n=10 (even), immediately identify the 5th and 6th terms from the ordered list to find the average.
Failing to arrange the numbers in ascending order before picking the middle terms is the most frequent error.
Arrange in Ascending Order
List the given data in non-decreasing order: 12, 12, 12, 23, 34, 45, 56, 67, 89, 90.
12,12,12,23,34,45,56,67,89,90
Identify Middle Terms
Since n=10 is even, the median is the average of the 5th and 6th terms.
5th=34,6th=45
Calculate Median
Apply the formula for an even number of terms: Median=(34+45)/2=79/2.
Median=234+45тАЛ=39.5
B is correct because the average of the 5th term (34) and 6th term (45) in the sorted data set is 39.5.
This concept is foundational for understanding 'Mean-Median-Mode' relationships and Skewness in Probability and Statistics sections.
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