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The median of the data set: 12, 15, 11, 19, 14, 18, 16 is:
15
14
16
18
15
Arrange the numbers in ascending order mentally by picking the smallest, then strike one from each end until you reach the middle element.
The data set provided is: 12, 15, 11, 19, 14, 18, 16. Total number of observations (n) is 7.
Median=(2n+1тАЛ)th┬аobservation┬а(for┬аodd┬аn)
Arrange the numbers in ascending order mentally by picking the smallest, then strike one from each end until you reach the middle element.
Students often forget to sort the data in ascending or descending order before picking the middle value, leading to incorrect answers based on the unsorted list.
Sort the data
Arrange the given set of numbers in ascending order: 11, 12, 14, 15, 16, 18, 19.
11,12,14,15,16,18,19
Identify number of terms
Count the number of observations in the set, which is n=7. Since 7 is an odd number, we use the formula for the middle position.
n=7
Calculate the median position
Find the position of the median using the formula 2n+1тАЛ. Substituting n=7, we get 27+1тАЛ=4.
rac7+12=4
Find the median value
Locate the 4th value in the sorted list: 11 (1st), 12 (2nd), 14 (3rd), 15 (4th).
Median=15
A is correct because the 4th observation in the sorted sequence 11, 12, 14, 15, 16, 18, 19 is 15.
This method is the foundation for finding quartiles and percentiles in grouped frequency distributions encountered in more advanced statistics sections.
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