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What is the median of the data: 12, 15, 11, 19, 14?
14
15
12
19
14
Arrange the numbers in ascending order mentally by picking the smallest and largest values to narrow down to the middle one.
The data set is 12, 15, 11, 19, 14. The total number of observations (n) is 5.
Median=(2n+1тАЛ)th┬аobservation┬аfor┬аodd┬аn
Arrange the numbers in ascending order mentally by picking the smallest and largest values to narrow down to the middle one.
Students often forget to arrange the data in ascending or descending order before identifying the middle term, leading them to choose the middle term of the unsorted list.
Sort the data
To find the median, first arrange the observations in ascending order: 11, 12, 14, 15, 19.
11,12,14,15,19
Identify n
Count the total number of observations. Here, n=5, which is an odd number.
n=5
Calculate the position
Since n is odd, the median is the value at the 2n+1тАЛ position.
Position=25+1тАЛ=3rd┬аterm
Select the median
The 3rd term in the sorted sequence 11, 12, 14, 15, 19 is 14.
Median=14
A is correct because after arranging the data in ascending order (11, 12, 14, 15, 19), the middle observation is 14.
Understanding the median is crucial for skewness and box-plot analysis in advanced statistics and data interpretation.