Question

I need help find the mode n median and the standard deviation please and thank you

Answer 1

Here The data set is given as,

`10,\text{ 16, 7, 6, 20, 5, 9, 12, 7}`

The mean of n observation is given as,

`Mean\text{ = }\frac{Sum\text{ of n observation }}{n}`

The mean is calculated as,

`\begin{gathered} Mean\text{ = }(10+16+7+6+20+5+9+12+7)/(9) \\ Mean\text{ = }(92)/(9) \\ Mean\text{ = 10.22} \end{gathered}`

Arranging the given observation in ascending order,

`5,\text{ 6, 7, 7, 9, 10, 12, 16, 20}`

Here n is 9 which is odd. Therefore median for the odd number of observations is calculated as,

`\begin{gathered} Median\text{ = }(n+1)/(2)^(th)observation \\ Median\text{ = }\frac{9\text{ + 1}}{2}^{th\text{ }}observation \\ Median\text{ = 5}^(th)\text{ observation} \end{gathered}`

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.