U.S. wine export markets.The Center for International Trade Development (CITD), provides a listing of the top 30 U.S. export markets for sparkling wines. Data on the amount exported (thousands of dollars) and 3-year percentage change for the 30 countries in a recent year are saved in the WINEXfile. (Data for 5 countries are listed in the table.) Descriptive statistics for these variables are shown in the Minitab printout (next column).

5 of the Top 30 U.S. Sparkling Wine Export Markets

Country	Export ($ Thousands)	3-Year Change (%)
Canada Japan Mexico Cayman Islands United Kingdom	4952 3714 2104 1576 1041	71.9% -16.9 143.2 280.7 465.8

a.Locate the mean amount exported on the printout and practically interpret its value.

b.Locate the median amount exported on the printout and practically interpret its value.

c.Locate the mean 3-year percentage change on the printout and practically interpret its value.

d.Locate the median 3-year percentage change on the printout and practically interpret its value.

Descriptive Statistics: Exports, Change
Variable	N	N*	Mean	St Dev.	Min.	Q1	Median	Q3	Max.	IQR
Export Change	30 28	0 2	653 481	1113 1098	70 -49	105 21	231 156	523 499	4952 5750	418 478

e. Use the information on the printout to find the range of the amount exported.

f.Locate the standard deviation of the amount exported on the printout.

g.Use the result, part f, to find the variance of the amount exported.

h.If one of the top 30 countries is selected at random, give an interval that is likely to include the export amount for this country.

Step by step solution

01

 Step 1: Locating and interpreting the mean amount exported

Mean Export = $ 653 thousand

We interpret that, on average, the top 5 wine exporting countries exported wines worth at least $653 thousand.

02

Finding and analyzing the median amount exported

Median Export = $231 thousand

50% of countries exported vines below $231 thousand, and 50% of countries exported vines worth above $231 thousand.

03

Identifying and Explaining the mean 3-year percentage change 

Mean % change = 481%

The average 3-year percentage change in wine exports for the top 5 countries is approximately 481%.

04

Figuring out and Understanding the median 3-year percentage change 

Median % change = 156%

Half of the countries saw a 3-year percentage change below 156%, and the rest witnessed a 3-year percentage change of more than 156%.

05

Computing the range of amount exported

Minimum = $70,000

Maximum = $4,952,000

$\begin{array}{c}\text{Range}=\text{Maximum}–\text{Minimum}\\ =\text{4952}000–\text{7}0,000\\ =\$\text{4},\text{882},000\end{array}$

Therefore, the range of the amount exported is $4,882,000.

06

Detecting the Standard Deviation of the amount exported

StDev = $1,113,000

07

Calculating the variance

$\begin{array}{c}\text{Standarddeviation=}\sqrt{\text{Variance}}\\ \text{Variance=}{\left(\text{Standarddeviation}\right)}^{\text{2}}\\ {\text{=(1113000)}}^{\text{2}}\\ \text{=1,238,769,000,000}\end{array}$

Therefore, variance = 1,238,769,000,000

08

Finding the interval where one of the top 30 countries might lie

Because we are looking at one of the top 30 countries, we assume that it should lie in the 3 standard deviations range from the mean. Therefore, it should lie between $\overline{\mathrm{x}}\pm 3\mathrm{s}$.

localid="1651318274398" $$\begin{gathered} \text{Lowerrange=}\stackrel{-}{\chi }\text{-3}\left(\text{IQR}\right) \\ =\text{653}-\text{3}\left(418\right) \\ =\text{653}-\text{1254} \\ =-\text{\$601} \end{gathered}$$

localid="1651318278676" $$\begin{gathered} \text{Upperrange=}\stackrel{-}{\chi }\text{+3}\left(\text{IQR}\right) \\ =\text{653+3}\left(418\right) \\ =\text{653+1254} \\ =\text{\$1,907} \end{gathered}$$

Therefore, one of the top 30 countries should lie between -$601,000 and $1,907,000.

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