91影视

A sample of prices of 鈥榖est buy鈥� TVs, which are equal to or greater than 60 inches, is given.

The sample size (n) is 12.

The measures of variation are computed to gain an insight into thedegree of variation present in a sample. The values are used to analyze and infer other important statistical characteristics of the data.

Range,variance$\left(s^2\right),$ andstandard deviation$\left(s\right)$ are the three basic measures of dispersion/variation that are frequently reported in statistical research.

Calculations done for the given dataset are shown below:

The range is calculated as

$$\begin{gathered} \text{Range}=\text{Maximum}\text{Value}-\text{Minimum}\text{Value} \\ =1800-950 \\ =850.0 \end{gathered}$$

Therefore, the sample range for the prices of TVs is equal to $850.0.

The formula of the sample variance is

$s^2=\frac{{鈭�}_{i=1}^n{\left(x_i-\stackrel{炉}{x}\right)}^2}{n-1}$

Here,

x represents the values in the sample, and

$\stackrel{炉}{x}$represents the mean of the sample.

The sample mean is calculated as

$$\begin{gathered} \stackrel{炉}{x}=\frac{{鈭�}_{1=1}^n{x}_i}{n} \\ =\frac{1800+1500+...+1750}{12} \\ =\frac{17450}{12} \\ 鈮�1454.2 \end{gathered}$$

.

Thus, the sample mean is $1454.2.

The sample variance is calculated as

$$\begin{gathered} s^2=\frac{{鈭�}_{i=1}^n{\left(x_i-\stackrel{炉}{x}\right)}^2}{n-1} \\ =\frac{{\left(1800-1454.2\right)}^2+{\left(1500-1454.2\right)}^2+...{\left(1750-1454.2\right)}^2}{12-1} \\ =\frac{672291.67}{11} \\ 鈮�61117.4 \end{gathered}$$

Therefore, the sample variance for the prices of TVs is equal to 61117.4${\left(\text{dollars}\right)}^2$.

The sample standard deviation is calculated as

$$\begin{gathered} s=\sqrt{s^2} \\ =\sqrt{61117.4} \\ 鈮�247.2 \end{gathered}$$

Therefore, the sample standard deviation for the prices of TVs is equal to $247.2.

The sample contains prices of only the 鈥榖est buy鈥� TVs. Thus, it cannot be considered a representative of the entire population of TVs equal to or greater than 60 inches.

Therefore, the measures of variation are not typical for all the TVs that are equal to or greater than 60 inches.