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What is the median of the following data set: 12, 15, 11, 19, 14, 18, 13?
14
15
13
16
14
Arrange the numbers in ascending order and simply strike out one number from each end (left and right) simultaneously until you reach the single middle value.
A data set of 7 numbers: 12, 15, 11, 19, 14, 18, 13
Median=value┬аof┬а(2n+1тАЛ)th┬аobservation┬аfor┬аodd┬аn
Arrange the numbers in ascending order and simply strike out one number from each end (left and right) simultaneously until you reach the single middle value.
Many students forget to sort the data in ascending or descending order before picking the middle value, leading them to pick an incorrect number like 19 or 11.
Sort the data
To find the median, first arrange the given set in ascending order: 11, 12, 13, 14, 15, 18, 19.
11,12,13,14,15,18,19
Determine position
Count the number of observations (n). Here, n=7. Use the formula for the median position of an odd set of data: 2n+1тАЛ=27+1тАЛ=4.
27+1тАЛ=4th┬аposition
Identify median
Locate the 4th value in the sorted sequence: 11 (1st), 12 (2nd), 13 (3rd), 14 (4th).
Median=14
A is correct because when the set is arranged in ascending order (11, 12, 13, 14, 15, 18, 19), the middle value is 14.
If the number of observations n were even, the median would be the average of the two central terms, which is a common follow-up question in Statistics.
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