The number of goals scored by Lionel Messi in the La Liga for 6 seasons from 2011-17 are tabulated below. Find the mean number of goals scored per season using the assumed mean method.

$\begin{matrix} S e a s o n & N u m b e r o f g o a l s 2011 - 12 & 50 2012 - 13 & 46 2013 - 14 & 28 2014 - 15 & 43 2015 - 16 & 26 2016 - 17 & 37 \end{matrix}$

35.4

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38.3

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39.5

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Solution

The correct option is B 38.3
Choose 37 as the assumed mean i.e A =37
Number of observations, N =6

$\begin{matrix} N u m b e r & D o f g o a l s (X) & (X - A) 50 & 13 46 & 9 28 & - 9 43 & 6 26 & - 11 37 & 0 \sum D = 8 \end{matrix}$

$M e a n g o a l s / s e a s o n = A + \frac{\sum D}{N} = 37 + \frac{8}{6} = 38.3 g o a l s / s e a s o n$

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\begin{matrix} S e a s o n & N u m b e r o f g o a l s 2011 - 12 & 50 2012 - 13 & 46 2013 - 14 & 28 2014 - 15 & 43 2015 - 16 & 26 2016 - 17 & 37 \end{matrix}

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