91Ó°ÊÓ

The units of measurement used here is dollars ($).

Dollars represent money and money is quantifiable. We can count money in numbers. Therefore, the data type is quantitative.

According to the Chebyshev’s rule, we know that,

1. Only few measurements fall in the first standard deviation from mean.
2. 75% measurements fall in the second standard deviation from mean.
3. 8/9 measurements fall in the third standard deviation from mean.
4. Any number k > 1, (1-1/k² ) measurements will fall in k standard deviation.

Mean () = $1500

Standard deviation (s) = $300

Minimum = $900

Maximum = $2100

To use rule 4, we need to find k,

$$\begin{gathered} \stackrel{\mathbf{¯}}{\mathbf{x}}\mathbf{+}\mathbf{ks}\mathbf{=}\mathbf{Max} \\ \mathbf{1500}\mathbf{+}\mathbf{k}\mathbf{\left(}\mathbf{300}\mathbf{\right)}\mathbf{=}\mathbf{2100} \\ \mathbf{k}\mathbf{\left(}\mathbf{300}\mathbf{\right)}\mathbf{=}\mathbf{600} \\ \mathbf{k}\mathbf{=}\frac{\mathbf{600}}{\mathbf{300}} \\ \mathbf{k}\mathbf{=}\mathbf{2} \end{gathered}$$

Now that we have k, we can use rule 4

$$\begin{gathered} \mathbf{1}\mathbf{-}\frac{\mathbf{1}}{{\mathbf{k}}^{\mathbf{2}}} \\ \mathbf{1}\mathbf{-}\frac{\mathbf{1}}{{\mathbf{2}}^{\mathbf{2}}} \\ \mathbf{1}\mathbf{-}\frac{\mathbf{1}}{\mathbf{4}} \\ \frac{\mathbf{3}}{\mathbf{4}} \end{gathered}$$

Therefore, ¾ of the measurements lie in 2 standard deviations.

Minimum = $600

Maximum = $2400

To use rule 4, we need to find k,

$$\begin{gathered} \stackrel{\mathbf{¯}}{\mathbf{x}}\mathbf{+}\mathbf{ks}\mathbf{=}\mathbf{Max} \\ \mathbf{1500}\mathbf{+}\mathbf{k}\mathbf{\left(}\mathbf{300}\mathbf{\right)}\mathbf{=}\mathbf{2400} \\ \mathbf{k}\mathbf{\left(}\mathbf{300}\mathbf{\right)}\mathbf{=}\mathbf{900} \\ \mathbf{k}\mathbf{=}\frac{\mathbf{900}}{\mathbf{300}} \\ \mathbf{k}\mathbf{=}\mathbf{3} \end{gathered}$$

Now that we have k, we can use rule 4

$$\begin{gathered} \mathbf{1}\mathbf{-}\frac{\mathbf{1}}{{\mathbf{k}}^{\mathbf{2}}} \\ \mathbf{1}\mathbf{-}\frac{\mathbf{1}}{{\mathbf{3}}^{\mathbf{2}}} \\ \mathbf{1}\mathbf{-}\frac{\mathbf{1}}{\mathbf{9}} \\ \frac{\mathbf{8}}{\mathbf{9}} \end{gathered}$$

Therefore, 8/9 of the measurements lie in 3 standard deviations.

Minimum = $1200

Maximum = $1800

To use rule 4, we need to find k,

$$\begin{gathered} \stackrel{\mathbf{¯}}{\mathbf{x}}\mathbf{+}\mathbf{ks}\mathbf{=}\mathbf{Max} \\ \mathbf{1500}\mathbf{+}\mathbf{k}\mathbf{\left(}\mathbf{300}\mathbf{\right)}\mathbf{=}\mathbf{1800} \\ \mathbf{k}\mathbf{\left(}\mathbf{300}\mathbf{\right)}\mathbf{=}\mathbf{300} \\ \mathbf{k}\mathbf{=}\frac{\mathbf{300}}{\mathbf{300}} \\ \mathbf{k}\mathbf{=}\mathbf{1} \end{gathered}$$

Therefore, none of the measurements lie in 1 standard deviation.

Minimum = $1500

Maximum = $2100

Because the minimum value here is the mean itself, we cannot say anything about the distribution.