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What is the median of the following data? 78, 33, 59, 56, 61, 36, 48, 42, 97, 57, 62
56.5
58
57
57.5
57
Arrange the numbers in ascending order and pick the middle-most element by cancelling pairs from the ends (5 elements from each side leave the 6th element).
Data: 78, 33, 59, 56, 61, 36, 48, 42, 97, 57, 62. Total observations (n) = 11.
Median=(2n+1тАЛ)th┬аobservation
Arrange the numbers in ascending order and pick the middle-most element by cancelling pairs from the ends (5 elements from each side leave the 6th element).
Forgetting to sort the numbers in ascending order first; taking the middle value of the unsorted list results in an incorrect answer.
Sort the data
Arrange the given numbers in ascending order: 33, 36, 42, 48, 56, 57, 59, 61, 62, 78, 97.
33,36,42,48,56,57,59,61,62,78,97
Apply median formula
Since the number of terms n=11 (which is odd), the median is the value at the position 2n+1тАЛ.
Position=211+1тАЛ=6th┬аposition
Identify the value
Look at the 6th position in the sorted list: the 1st is 33, 2nd is 36, 3rd is 42, 4th is 48, 5th is 56, and the 6th is 57.
Median=57
C is correct because after arranging the 11 numbers in ascending order, the 6th observation is 57.
This concept of median is essential for calculating 'Quartiles' and 'Percentiles' in advanced descriptive statistics problems.
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