In statistics and data analysis, understanding numeric concepts is very important. Most of the time, terms that appear similar can have different meanings and result to misinterpretations and erroneous conclusions. This is especially true when dealing with the concepts of percentage and percentile in diverse fields like education, finance or healthcare and research. Let us look at the terms percentage and percentile broadly.
What Is a Percentile?
In statistics, a percentile is a term that describes how a score compares to other scores from the same set. While there is no standard definition of percentile, it is commonly expressed as the percentage of values in a set of data scores that fall below a given value.
In other words a percentile is a number where a certain percentage of scores fall below the given number. For example, an 18-year-old male who is six and a half feet tall is in the 99th percentile for his height. This means that of all the 18-year-old males, 99 percent have a height that is equal to or less than six and a half feet.
The percentile formula is used when we need to compare the exact values or numbers over the other numbers from the given data i.e. the accuracy of the number. Often percentile and percentage are taken as one but both are different concepts. A percentage is where the fraction is considered as one term while percentile is the value below the percentage found from the given data. In our day-to-day life, percentile formulas are usually helpful in finding the test scores or biometric measurements.
Percentile Formula
Percentiles for the values in a given data set can be calculated using the formula:
n = (P/100) x N
where N = number of values in the data set, P = percentile, and n = ordinal rank of a given value (with the values in the data set sorted from smallest to largest).
What is Percentage?
In mathematics or statistics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, “%”, although the abbreviations “pct.”, “pct” and sometimes “pc” are also used. A percentage is a dimensionless number; it has no unit of measurement.
The term “percentage” is formed from two words: “per” and “cent.” Cent is a word with Latin and French origins that means “hundred,” and “percent” means “per hundred.”
In other words, percentage means “per 100” and denotes a piece of a total amount. For example, 45% represents 45 out of 100, or 45% of the total amount. Percentage may also be referred to as “out of 100” or “for every 100.” For example, you could say either “it snowed 20 days out of every 100 days” or “it snowed 20% of the time.”
Mathematically, percentages are either numbers or ratios that are expressed as fractions of 100. They are usually denoted as “%” or “percent.” An example of a percentage is 65% or 65 percent. They may be further represented as simple fractions or decimal fractions. Percentage calculations are important in business and various professional settings such as when calculating taxes or employee raises.
Percentage vs Percentile
| Percentage | Percentile |
| A mathematical unit of measurement that displays the answer out of a total of 100. | Percentile is a value from which the values of percentages below it are found. |
| The unit of percentage is denoted by % | The unit of percentile is denoted by xth, for example, 30th, |
| It does not have quartiles. | It has quartiles. |
| A percentage can be written in the form of ratios. | A percentile cannot be written in the form of ratios. |
| Percentages can also be written in the form of decimals. | Percentiles, on the other hand, cannot be written in the form of decimals. |
| Percentages are not based on the rank of numbers. | A percentile is based on the rank of numbers. |
| It is based on one case. | It is based on the comparison of one case with several cases. |
| It does not rely on the normal distribution. | Percentile relies on the normal distribution. |
Key Takeaways
- Percentiles are used to understand and interpret data. They indicate the values below which a certain percentage of the data in a data set is found.
- Percentiles can be calculated using the formula n = (P/100) x N, where P = percentile, N = number of values in a data set (sorted from smallest to largest), and n = ordinal rank of a given value.
- Percentiles are frequently used to understand test scores and biometric measurements.
- The term “percentage” was adapted from the Latin word “per centum”, which means “by the hundred”. Percentages are fractions with 100 as the denominator. In other words, it is the relation between part and whole where the value of whole is always taken as 100.
- Percent is another name for indicating hundredths. Thus, 1% is one-hundredth, that means 1%=1/100=0.01. In other words, Percentages can also be represented in decimal or fraction form, such as 0.6%, 0.25%, etc.
- Percentages have no dimension. Hence it is called a dimensionless number. If we say, 50% of a number, then it means 50 per cent of its whole.
- Percentage calculations are important in business and various professional settings such as when calculating taxes or employee raises.