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# In a mathematics test given to 15 students the following marks (out of 100) are recorded.

Q. 2.     In a mathematics test given to 15 students, the following marks (out of 100) are recorded:

41,     39,     48,     52,     46,     62,     54,     40,     96,     52,     98,     40,     42,     52,     60

Find the mean, median and mode of this data.

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

Number of observations, n = 15

$\\\bar{X}=\frac{\sum_{i=1}^{n=15}x_{i}}{n}\\ \bar{X}=\frac{41+ 39+ 48+ 52+ 46+ 62+ 54+ 40+ 96+ 52+ 98+ 40+ 42+ 52+ 60}{15}\\ \bar{X}=\frac{822}{15}\\ \bar{X}=54.8$

Mean is 54.8

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

39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98

n = 15 (odd)

$\\Median=(\frac{n+1}{2})^{th}\ term\\ Median=(\frac{15+1}{2})^{th}\ term\\ Median=8^{th}\ term\\ Median=52$

In the given data 52 occurs the maximum number of times ()

Therefore, Mode = 52

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