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Find the median of the following data: 45, 22, 67, 34, 56, 89, 41, 12, 73, 50, 39.
41
45
50
56
45
Quickly group numbers by their tens digits to arrange them mentally, then pick the middle value directly.
Given data: 45, 22, 67, 34, 56, 89, 41, 12, 73, 50, 39
Median=value┬аof┬а(2n+1тАЛ)th┬аterm
Quickly group numbers by their tens digits to arrange them mentally, then pick the middle value directly.
Failing to sort the data in ascending order before locating the middle term leads to incorrect results.
Step 1: Count and Sort Data
Count the total number of observations, which is n=11 (an odd number), and arrange the data in ascending order.
12,22,34,39,41,45,50,56,67,73,89
Step 2: Apply the Median Formula for Odd n
For an odd number of observations, the median is the value of the (2n+1тАЛ)-th term.
Position=211+1тАЛ=6th┬аterm
Step 3: Find the Value
Identify the 6th term in the sorted sequence, which is 45.
Median=45
B is correct because after arranging the 11 data points in ascending order, the 6th term is 45.
Median is robust against extreme outliers compared to the mean, making it a crucial metric in skewed distributions.
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