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Find the median of the following data set: 12, 45, 23, 89, 34, 12, 56, 78, 23, 44.
34
39
44
45
39
Arrange the numbers quickly by picking the smallest and largest, canceling them out, and moving toward the center until only the two middle numbers remain.
A set of 10 observations: 12, 45, 23, 89, 34, 12, 56, 78, 23, 44.
Median=2Value┬аof┬а(2nтАЛ)th┬аobservation+Value┬аof┬а(2nтАЛ+1)th┬аobservationтАЛ
Arrange the numbers quickly by picking the smallest and largest, canceling them out, and moving toward the center until only the two middle numbers remain.
Students often forget to arrange the data in ascending order before finding the median and mistakenly calculate the median of the unsorted list.
Sorting the Data
Arrange the given 10 numbers in ascending order: 12, 12, 23, 23, 34, 44, 45, 56, 78, 89.
12,12,23,23,34,44,45,56,78,89
Identifying Middle Terms
Since the total number of observations n=10 is even, the median is the average of the 5th and 6th terms.
n=10тЯ╣Median=2x5тАЛ+x6тАЛтАЛ
Calculating Median
The 5th value is 34 and the 6th value is 44. Calculating their average gives the median.
Median=234+44тАЛ=278тАЛ=39
B is correct because the average of the 5th (34) and 6th (44) terms in the ordered set is 39.
This concept is a precursor to understanding Quartiles, Deciles, and Percentiles in statistics, which are often tested in competitive exams under the 'Measures of Central Tendency' header.
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