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Mikka · Answer 1 · 2023-09-14T13:27:03+0000

Mean)

In general, the formula is

$\operatorname{mean}=\frac{\text{ sum of elements in the dataset}}{\text{ number of elements in the dataset}}$

Thus, in our case,

$\begin{gathered} \Rightarrow X=\operatorname{mean}=(4.85+5.10+5.50+4.75+4.5+5+6)/(7) \\ \Rightarrow X=\operatorname{mean}=5.1 \end{gathered}$

Thus, the mean is 5.1

Variance)

In general, the formula is

$\text{Variance}=S^2=\sum ^{}_{}((x_i-X)^2)/(N-1)$

Where x_i is each of the elements in the data set, X is the mean, and N is the number of elements in the data set.

Therefore, in our case,

$\begin{gathered} N=7,X=5.1 \\ \Rightarrow S^2=(1)/(7-1)((4.85-5.1)^2+(5.1-5.1)^2+(5.5-5.1)^2+(4.75-5.1)^2+(4.5-5.1)^2+(5-5.1)^2+(6-5.1)^2) \\ \Rightarrow S^2=0.2541666\ldots \\ \Rightarrow S^2\approx0.254 \end{gathered}$

The variance is 0.254

Standard deviation)

If S^2 is the variance; then,

$\text{ standard deviation}=\sigma=\sqrt[]{S^2}$

Hence, in our case,

$\begin{gathered} \Rightarrow\sigma=\sqrt[]{0.2541666\ldots}\approx0.504149\ldots \\ \Rightarrow\sigma\approx0.504 \end{gathered}$

The standard deviation is 0.504

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