Chapter 1.2, Problem 38E

(a)

To determine

To make: a dotplot to display these data and describe the pattern of the distribution and deviations

Answer to Problem 38E

Shape: the data is right-skewed, because the highest dots are to the left of the dotplot.

Centre: it is about 0 gold medals, because the highest dots are at 0 in the dotplot.

Spread: it is from $0$ hours to $51$ gold medals.

Outliers: There are three outliers in the data; these are the values of China, Great Britain and the United States.

Explanation of Solution

Given:

Country	Gold medals
Sri anka	$0$
China	$51$
Vietnam	$0$
Great Britain	$19$
Norway	$3$
Romania	$4$
Switzerland	$2$
India	$0$
Georgia	$3$
Kyrgyzstan	$0$
Costa Rica	$0$
Brazil	$3$
Uzbekistan	$1$
Thailand	$2$
Kuwait	$0$
Bahamas	$0$
Kenya	$5$
Trinidad and Tobago	$0$
Greece	$0$
Mozambique	$0$
Kazakhstan	$2$
Denmark	$2$
Latvia	$1$
Czech Republic	$3$
Hungary	$3$
Sweden	$0$
Uruguay	$0$
United States	$36$

Calculation:

Here we have the data of the total number of gold medals won by a randomly selected sample of countries as follows:

Country	Gold Medals
	$0$
	$51$
	$0$
	$19$
	$3$
	$4$
	$2$
	$0$
	$3$
	$0$
	$0$
	$3$
	$1$
	$2$
	$0$
	$0$
	$5$
	$0$
	$0$
	$0$
	$2$
	$2$
	$1$
	$3$
	$3$
	$0$
	$0$
	$36$

Dot Plot is one of the simplest graph that shows each data value as a dot above its location on number line. The dot plot for given data is below:

Country	Gold medals
Sri anka	$0$
China	$51$
Vietnam	$0$
Great Britain	$19$
Norway	$3$
Romania	$4$
Switzerland	$2$
India	$0$
Georgia	$3$
Kyrgyzstan	$0$
Costa Rica	$0$
Brazil	$3$
Uzbekistan	$1$
Thailand	$2$
Kuwait	$0$
Bahamas	$0$
Kenya	$5$
Trinidad and Tobago	$0$
Greece	$0$
Mozambique	$0$
Kazakhstan	$2$
Denmark	$2$
Latvia	$1$
Czech Republic	$3$
Hungary	$3$
Sweden	$0$
Uruguay	$0$
United States	$36$

The overall pattern of the distribution can be described by its shape, center, spread and outliers.

Shape: The Dot plot has its peak at $0$ this means that maximum sample countries did not won any gold. Thus $0$ is the mode. Most of the countries have won gold medals between $0$ to $3$ . However, distribution has a long tall towards right.

Centre: We can describe centre by finding a value that divides the observations. So that about half take larger values and about half take smaller values. This is called Median of the distribution which is $3$ for this data. We can also calculate the mean no of hours that is $4.9$ for this data.

Spread: The spread of the distribution tells us how much variability there is in the data. One way to describe the variability is to give the smallest and the largest values. The spread of given data is from $0$ hours to $51$ hours. The range can be calculated by subtracting smallest value from largest value from largest value.

  $51$ Gold medals- $0$ gold medals= $51$ gold medals

Outliers: The values that differ from the overall pattern and stand clearly apart from the rest of the distribution. $19,36$ and $51$ are the outliers. The presence of outliers has lead to difference in mean median and mode.

Mean $(4.9)$ is greater than Median $(3)$ , which is greater than Mode $(0)$ .

Conclusion:

Shape: the data is right-skewed, because the highest dots are to the left of the dotplot.

Centre: it is about 0 gold medals, because the highest dots are at 0 in the dotplot.

Spread: it is from $0$ hours to $51$ gold medals.

Outliers: There are three outliers in the data; these are the values of China, Great Britain and the United States.

(b)

To determine

To find: whether the sample of countries listed in the table is representative of this larger population or not

Answer to Problem 38E

The given sample does not represent the 2008 Summer Olympics.

Explanation of Solution

Calculation:

Here we have the data of the total number of gold medals won by a randomly selected sample of countries as follows:

Country	Gold Medals
	$0$
	$51$
	$0$
	$19$
	$3$
	$4$
	$2$
	$0$
	$3$
	$0$
	$0$
	$3$
	$1$
	$2$
	$0$
	$0$
	$5$
	$0$
	$0$
	$0$
	$2$
	$2$
	$1$
	$3$
	$3$
	$0$
	$0$
	$36$

Here we have informed that in the 2008 Summer Olympic, $55$ of the $204$ participated countries have won at least one gold medal. By definitions, the proportion of the countries that have won at least one gold medal is given as

  

In the given sample of $30$ countries, we observe that $17$ countries have won at least one gold medal. By definitions, the proportion of the countries that have won at least one gold medal is given as $\frac{55}{204}=26.96\%$ .

Therefore, the given sample does not represent the 2008 Summer Olympics.

Conclusion:

Therefore, the given sample does not represent the 2008 Summer Olympics.