Here The data set is given as,
[tex]10,\text{ 16, 7, 6, 20, 5, 9, 12, 7}[/tex]
The mean of n observation is given as,
[tex]Mean\text{ = }\frac{Sum\text{ of n observation }}{n}[/tex]
The mean is calculated as,
[tex]\begin{gathered} Mean\text{ = }\frac{10+16+7+6+20+5+9+12+7}{9} \\ Mean\text{ = }\frac{92}{9} \\ Mean\text{ = 10.22} \end{gathered}[/tex]
Arranging the given observation in ascending order,
[tex]5,\text{ 6, 7, 7, 9, 10, 12, 16, 20}[/tex]
Here n is 9 which is odd. Therefore median for the odd number of observations is calculated as,
[tex]\begin{gathered} Median\text{ = }\frac{n+1}{2}^{th}observation \\ Median\text{ = }\frac{9\text{ + 1}}{2}^{th\text{ }}observation \\ Median\text{ = 5}^{th}\text{ observation} \end{gathered}[/tex]
Thus the median is 9.
Mode refers to the observation which occurs a maximum number of times in the given dataset.
Therefore the mode is 7.
The standard deviation of the given dataset is 4.71.
