Chapter 10.1, Problem 6CYU

i.

To determine

To calculate the percentile rank for the United States.

Answer to Problem 6CYU

The percentile rank of United States is 90

Explanation of Solution

Given information:

Data of medals counts of some countries

Country	Total
Belarus	6
France	15
Austria	17
Norway	26
Russia	33
Switzerland	11
Netherlands	24
United states	28
Germany	19
Canada	25

Formula Used:

  $percentile=\frac{NumberOfValuesBeforeX}{n}\times 100$

Calculation:

Re-arranging the countries in an ascending orders of their medals,

Country	Medals
Belarus	6
Switzerland	11
France	15
Austria	17
Germany	19
Netherlands	24
Canada	25
Norway	26
United states	28
Russia	33

For percentile,

Substituting the values in the percentile formula,

  $percentile=\frac{9}{10}\times 100$

On solving,

  $percentile=90$

Hence, United States is at 90^th percentile.

Conclusion: United States is at 90 percentile.

ii.

To determine

To calculate which countries are below 50^th percentile?

Answer to Problem 6CYU

Austria, France, Switzerland and Belarus are above 50^th percentile

Explanation of Solution

Given information: Data of medals of all countries

Country	Medals
Belarus	6
Switzerland	11
France	15
Austria	17
Germany	19
Netherlands	24
Canada	25
Norway	26
United states	28
Russia	33

Formula Used:

  $ValueOfX=\frac{percentile}{100}\times (n+1)$

Calculation:

Substituting the values in the formula,

  $x=\frac{50}{100}\times (9+1)$

So,

  $x=\frac{50}{100}\times (10)$

On solving,

  $x=5$

Comparing the value to the table,

Austria, France, Switzerland and Belarus are above 50^th percentile

Conclusion: Austria, France, Switzerland and Belarus are above 50^th percentile

iii.

To determine

To calculate which countries are above 70^th percentile?

Answer to Problem 6CYU

Netherlands, Germany, Austria, France, Switzerland and Belarus are above 70^th percentile

Explanation of Solution

Given information: Data of medals of some countries

Country	Medals
Belarus	6
Switzerland	11
France	15
Austria	17
Germany	19
Netherlands	24
Canada	25
Norway	26
United states	28
Russia	33

Formula Used:

  $ValueOfX=\frac{percentile}{100}\times (n+1)$

Calculation:

Substituting the values in the formula,

  $x=\frac{70}{100}\times (9+1)$

So,

  $x=\frac{70}{100}\times (10)$

On solving,

  $x=7$

Comparing the value to the table,

Netherlands, Germany, Austria, France, Switzerland and Belarus are above 70^th percentile

Conclusion: Netherlands, Germany, Austria, France, Switzerland and Belarus are above 70^th percentile