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Question
The points scored by a basket ball team in a series of matches are as follows:
17, 2, 7, 27, 25, 5, 14, 18, 10, 24, 48, 10, 8, 7, 10, 28
Find the median and mode for the data.
Solution
Consider the data set:
17, 2, 7, 27, 25, 5, 14, 18, 10, 24, 48, 10, 8, 7, 10, 28
Let arrange the given points scored in ascending order, we get:
2, 5, 7, 7, 8, 10, 10, 14, 17, 18, 24, 25, 27, 28, 48
Number of given observations in this data set is 16 that is even.
So, median will be calculated as follows:
Median = `((n/2)^(th) "observation" + (n/2 + 1)^(th) "observation")/2`
= `((16/2)^(th) "observation" + (16/2 + 1)^(th) "observation")/2`
= `((8)^(th) "observation" + (9)^(th) "observation")/2`
= `(10 + 14)/2`
= `24/2`
= 12
As we know that, mode is the observation which is repeated maximum number of times that is 10.
Hence, median and mode for the given data are 12 and 10, respectively.
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