#### Chapter 11 Language of Descriptive Statistics

Section 11.2 Frequency Distributions and Percentage Calculation

# 11.2.2 Percentage Calculation

In descriptive statistics, numerical values are often specified in percentages, so we will review the most relevant elements of percentage calculations in this section. Numbers given as percentages ("percent, hundredth") serve to illustrate ratios and to make them comparable by putting the numbers into relation to a unified base value (hundred).
##### Info 11.2.5

Let $a\ge 0$ be a real number. Then, we have $a %=\frac{a}{100}$, i.e. the symbol $%$ can be interpreted as "divided by 100" (just as the symbol $\circ$ with respect to angles was interpreted in Module 5 as a multiplication by $\frac{\pi }{180}$).

For example:
• One percent is one hundredth: $1 %=\frac{1}{100}=0.01$
• Ten percent is one tenth: $10 %=\frac{10}{100}=0.1$
• 25 percent is one quarter: $25 %=\frac{25}{100}=0.25$
• One hundred percent is a whole: $100 %=\frac{100}{100}=1$
• 150 percent is a factor of 1.5: $150 %=\frac{150}{100}=1.5$

In general, percentages describe ratios and relate to a certain base value. The base value is the initial value the percentage relates to. The percentage is expressed in percent and denotes a ratio with respect to the base value. The real value of this quantity is called the percent value. The percent value has the same unit as the base value.
##### Info 11.2.6

The rule of three applies for the percent value, base value and percentage :

$\text{percentage}\mathrm{ }·\mathrm{ }\text{base value}\mathrm{ }\mathrm{ }=\mathrm{ }\mathrm{ }\text{percent value} .$