The term percentage or symbol % is used frequently in everyday language and life. For example, it is common to see sales with 20% discount, or restaurant bills with 10% service charges, as well as reports in newspapers discussing tax, unemployment and other values in percentage terms.
Percentage means parts out of 100 and is the same as a fraction with a denominator (base or the bottom) of 100. Therefore:
- 15% means 15 parts out of 100 and is the same as the fraction 15/100
- 87% means 87 parts out of 100 and is the same as the fraction 87/100
A further way of expressing parts out of 100 is using a decimal and so percentages can also be expressed as decimals:
- 15% is the same as 0.15 or 15/100
- 87% is the same as 0.87 or 87/100
There are three main ways in which percentages are frequently used:
- to show the share of something from a total;
- to quantify the amount of change over time;
- to express an increase or reduction, as it creates a common baseline to make the figures comparable.
- Showing the share from a total
The very first function of percentage is showing the share of smaller items from a total or baseline.
We have four apples. Two apples are red and the other two are green. This means that 50% of apples are red.
In this example the “four apples” are considered “the total”. The percentage shows the share of smaller items, i.e. two red and two green apples from the total apples.
Now we have 5 apples, one red and the other four green. In order to calculate the share of red apples from total apples:
(The number of red apples/ the total number of apples)x100
(1/5)x100=20
So 20% of the apples are red.
Now look at this example:
According to official data, 824,000 people participated in university entrance exam in 2012-13. Data also shows that 316,000 participants were male.
We can use percentage to make the figures more understandable:
(316,000/824,000)x 100 = 38.34
Therefore,
In 2012-13, about 38.1% of participants were male.
Don’t worry about calculations, there is no need to use them in your exam sessions.
Now let’s work on another example
(Example 2) In the 2013-14 university entrance exam, the total number of participants was 1,076,300. Official data shows that the number of male participants was 413,500.
(413,500/ 1,076,300 )x100= 38.41%
Therefore, male students accounted for 38.4% of Konkoor participants in 2013-14.
The two percentages clarify the key difference between values (316,000 in example 1, and 413,500 in example 2) and the share of values from a total (expressed in percentage).
As you see, despite the fact that the number of male participants in 2013-14 was 98,000 more than that of 2012-13; the share of male participants was quite unchanged.
Note that the sum of percentages equals 100% when we use percentage for presenting the share of something from a total. The 100% is the baseline or the total.
Exercise: Calculate the share of female participants in example 1 and 2.
Using percentages to compare information
Whilst researching for an essay or dissertation you may come across many sources of data in tables, graphs or reports which you would like to incorporate into your work. However, this can be difficult if they do not share a common base line.
Percentages are useful for comparing information where the sample sizes or totals are different. By converting different data to percentages you can readily compare them.
Give bases of all percentages
Because percentages are always derived from a specific base, they are meaningless until associated with a base. So even if I tell you that after reading this handout, you will be 23% more persuasive as a writer, that is not a very meaningful assertion, because you have no idea what it is based on—23% more persuasive than what?
Examples
- 70% of those who were interviewed indicated that …
- Since 1981, England has experienced an 89% increase in crime.
- The response rate was 60% at six months and 56% at 12 months.
- In 1960 just over 5% of live births in 1960 were outside marriage.
- Returned surveys from 34 radiologists yielded a 34% response rate.
- He also noted that fewer than 10% of the articles included in his study cited …
- With each year of advancing age, the probability of having X increased by 9.6% (p = 0.006).
- The mean income of the bottom 20 percent of U.S. families declined from $10,716 in 1970 to …
- X found that of 2,500 abortions, 58% were in young women aged 15-24, of whom 62% were …