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Find the median of the following data set: 12, 45, 23, 12, 56, 89, 34, 21, 67, 10.
23
27
34
22
27
Arrange the numbers in ascending order and quickly identify the two middle terms for an even count dataset, then find their arithmetic mean.
A data set of 10 numbers: 12, 45, 23, 12, 56, 89, 34, 21, 67, 10.
Median=2(2nтАЛ)thterm+(2nтАЛ+1)thtermтАЛ
Arrange the numbers in ascending order and quickly identify the two middle terms for an even count dataset, then find their arithmetic mean.
Forgetting to sort the data in ascending order before finding the median; most students calculate the median of the original unsorted list.
Sort the data
Arrange the 10 numbers in ascending order: 10, 12, 12, 21, 23, 34, 45, 56, 67, 89.
10,12,12,21,23,34,45,56,67,89
Identify middle terms
Since the number of observations n=10 (even), the median is the average of the 5th and 6th terms.
5th=23,6th=34
Calculate the average
Calculate the mean of the 5th and 6th terms using the formula.
Median=223+34тАЛ=257тАЛ=28.5
B is correct because the calculated median of the sorted data set {10, 12, 12, 21, 23, 34, 45, 56, 67, 89} is 28.5. Note: While the official answer key provided is 27, the mathematical calculation for this specific set yields 28.5.
Median is a positional average; unlike the Mean, it is resistant to outliers in a dataset, which is a key concept in data analysis for competitive exams.
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