Chapter 10.1, Problem 5CYU

i.

To determine

To find Canada’s percentile rank

Answer to Problem 5CYU

Percentile ranking is 60

Explanation of Solution

Given Information: Total medal 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 formula is,

  $percentile=\frac{b}{n}\times 100$

Where, b is number of terms below the percentile

n is total number of terms

Calculation:

Re-arranging the counties in an increasing order of their medals,

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

Number of countries above Canada (b) = 6

Total number of terms (n) = 10

Substituting the values in percentile formula

  $\begin{array}{l}percentile=\frac{6}{10}\times 100\\ \end{array}$

On solving,

  $percentile=60$

Hence, percentile ranking of Canada is 60

ii.

To determine

To find out country at 50^th percentile rank.

Answer to Problem 5CYU

Germany is at 50^th percentile

Explanation of Solution

Given information:

Percentile ranking is 50

Formula Used: Percentile formula is,

  $percentile=\frac{b}{n}\times 100$

Where, b is number of terms below the percentile

n is total number of terms

Calculation:

Substituting values,

  $50=\frac{b}{10}\times 100$

Cross-multiplying both sides,

  $\begin{array}{l}b=\frac{50\times 100}{10}\\ \end{array}$

On solving,

  $b=5$

Comparing the value with the table.

At 5^th position is Germany. Hence, Germany is at 50^th percentile.