Find the median, mean and mode of the given data.
7, 8, 12, 10, 9, 8, 9, 11, 8, 11, 8

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Solution

$The given data is, 7, 8, 12, 10, 9, 8, 9, 11, 8, 11, 8 . Number of observations, n = 11 Sum of observations = 7 + 8 + 12 + 10 + 9 + 8 + 9 + 11 + 8 + 11 + 8 = 101 Mean = \frac{sum of observations}{number of observations} = \frac{101}{11} = 9.18 The given data is, 7, 8, 12, 10, 9, 8, 9, 11, 8, 11, 8 . By inspection, we see that the observation 8 occurs most frequently that is 4 times in the data set . So, the mode of the given data is 8 . Arranging the data in ascending order, we get 7, 8, 8, 8, 8, 9, 9, 10, 11, 11, 12 . Number of observations, n = 11, which is odd . So, median = value of {(\frac{n + 1}{2})}^{th} observation \Rightarrow median = value of {(\frac{11 + 1}{2})}^{th} observation \Rightarrow median = value of 6^{th} observation \Rightarrow median = 9$

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