Q. 1.     The following number of goals were scored by a team in a series of 10 matches:

             2,         3,         4,         5,         0,         1,         3,         3,         4,         3

            Find the mean, median and mode of these scores.

Answers (1)

Mean=\frac{Sum\ of\ observations}{Number \ of\ observations}

Number of observations, n = 10

\\\bar{X}=\frac{\sum_{i=1}^{n=10}x_{i}}{n}\\ \bar{X}=\frac{ 2+ 3+ 4+ 5+ 0+ 1+ 3+ 3+ 4+ 3}{10}\\ \bar{X}=\frac{28}{10}\\ \bar{X}=2.8

Mean is 2.8

To find the median we have to arrange the given data in ascending order as follows:

0, 1, 2, 3, 3, 3, 3, 4, 4, 5

n = 10 (even)

\\Median=\frac{(\frac{n}{2})^{th}\ term+(\frac{n}{2}+1)^{th}\ term}{2}\\ Median=\frac{(\frac{10}{2})^{th}\ term+(\frac{10}{2}+1)^{th}\ term}{2}\\ Median=\frac{(5)^{th}\ term+(6)^{th}\ term}{2}\\ Median=\frac{3+3}{2}\\ Median=3

In the given data 3 occurs the maximum number of times (4)

Therefore, Mode = 3

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