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Find the median of the data set: 10, 13, 14, 17, 18.
14
17
13
10
14
Since the data set is already sorted in ascending order, simply cancel out one number from each end iteratively until the central value remains.
The data set is 10, 13, 14, 17, 18.
Median=(2n+1тАЛ)th┬аterm,┬аwhere┬аn┬аis┬аthe┬аnumber┬аof┬аobservations.
Since the data set is already sorted in ascending order, simply cancel out one number from each end iteratively until the central value remains.
Many students try to calculate the mean (average) instead of the median, or they forget to sort the data in ascending order before picking the middle term.
Count the number of terms
Count the total number of observations in the set {10, 13, 14, 17, 18}.
n=5
Check if ordered
The data set is already arranged in ascending order: 10, 13, 14, 17, 18.
10<13<14<17<18
Apply Median formula
Since n is odd, use the formula Median=(2n+1тАЛ)th position.
25+1тАЛ=3rd┬аterm
Identify the value
The 3rd term in the sorted sequence 10, 13, 14, 17, 18 is 14.
Median=14
A is correct because the middle term of the ordered set {10, 13, 14, 17, 18} is 14.
This concept is foundational for understanding quartiles and box-plot constructions in higher-level statistics.