Answer:
Concept:
Mean is just another name for average. To find the mean of a data set, add all the values together and divide by the number of values in the set. The result is your mean!
The values are given below as
[tex]6,14,7,4,12,8,13,4,18,14[/tex]
The image below shows how to calculate the mean
By substituting values, we will have
[tex]\begin{gathered} \bar{x}=\frac{\sum ^{}_{n\mathop=0}x}{n} \\ n=10 \end{gathered}[/tex][tex]\begin{gathered} \bar{x}=\frac{6+14+7+4+12+8+13+4+18+14}{10} \\ \bar{x}=\frac{100}{10} \\ \bar{x}=10 \end{gathered}[/tex]
Hence,
The mean = 10
To calculate the variance, we will use the formula below
[tex]^{}\sigma^2=\frac{\sum ^{\infty}_{n\mathop=0}(x-\bar{x})^2}{n}[/tex][tex]\begin{gathered} \sigma^2=\frac{\sum ^{\infty}_{n\mathop{=}0}(x-\bar{x})^2}{n} \\ (x-\bar{x})^2=(6-10)^2+(14-10)^2+(7-10)^2+(4-10)^2+(12-10)^2+(8-10)^2+(13-10)^2+(4-10)^2+(18-10)^2+(14-10)^2 \\ (x-\bar{x})^2=16+16+9+36+4+4+9+36+64+16 \\ (x-\bar{x})^2=210 \end{gathered}[/tex][tex]\begin{gathered} \sigma^2=\frac{\sum ^{\infty}_{n\mathop{=}0}(x-\bar{x})^2}{n} \\ \sigma^2=\frac{210}{10} \\ \sigma^2=\frac{210}{10} \\ \sigma^2=21 \end{gathered}[/tex]
Hence
The variance = 21
To calculate the standard deviation,
[tex]\begin{gathered} \sigma=\sqrt[]{variance} \\ \sigma=\sqrt[]{21} \\ \sigma=4.58 \end{gathered}[/tex]
Hence,
The standard deviation is = 4.58
