how to calculate percentile – JDM Educational

Percentile is used in statistics to give us an idea of where a data value lies in relation to a group of data points. It is also useful for ranking purposes, but it is important to know how to interpret percentiles so you don’t misunderstand or misuse them. So, how do you interpret percentile? Percentile tells you the rank of an individual compared to the rest of the population. A percentile is a value that a percentage of the population falls below. The 50th percentile is the median, and tells us the value that separates the population into a top half and a bottom half. Of course, percentile depends entirely on the context of the population or group that you use. For example, you could be in the 50th percentile of weight for adult men, but the 85th percentile of weight for all adults. In this article, we’ll talk about percentile and how to interpret this concept. We’ll also give some examples and explain how percentile is related to z scores (for normal distributions). Let’s get started. How To Interpret Percentile A percentile (or percentile score) tells you the rank of an individual relative to the rest of the population. A percentile is a value that a percentage of the population falls below. More specifically, the value of the Nth percentile tells us that N percent of the population falls below that value. For example, in 2020, $141,000 was the 80th percentile household income in the U.S. An income of $141,000 puts you in the 80th percentile (top 20%) of household incomes in the U.S. in 2020. This means that 80% of households have an income below $141,000. It also means that 20% of households have an income of $141,000 or higher. So, a percentile score really tells us two things: The percentage of the population below that percentile score: N percent for the Nth percentile.The percentage of the population at or above that percentile score: 100 - N percent for the Nth percentile. What Does Percentile Mean In Weight? A weight percentile tells you what percentage of the population has a weight below that value. For example, the 30th percentile of weight for men in the U.S. is 170.2 pounds That means that 30 percent of men weigh less than 170.2 pounds, while 70 percent of men weigh 170.2 pounds or more. Keep in mind that for children, height and weight percentiles will depend on age, since children grow so fast when they are young. As a result, there is no single chart you can consult for this purpose. What Does 25th Percentile Mean? The 25th percentile tells you the value that 25% of the population falls below. Alternatively, it is the value that 75% of the population is at or above. The 25th percentile is the top of the bottom quartile of the population (a quartile is one-fourth). For example, the 25th percentile for the weight of U.S. women is 137.1 pounds. This means that a woman who weighs 137.1 pounds or less is in the bottom quartile (the bottom 25%, also called Q1) of the women in the U.S. If you are in the 25th percentile, that means you are above 25% of the population and below 75%. The 25th percentile is the top of the bottom quartile, Q1. What Does 50th Percentile Mean? The 50th percentile tells you the value that 50% of the population falls below. Alternatively, it is the value that 50% of the population is at or above. The 50th percentile is the top of the second quartile (Q2) of the population (a quartile is one-fourth). For example, the 50th percentile for the weight of U.S. women is 161.3 pounds. This means that a woman who weighs 161.3 pounds or less is in the bottom half (the bottom 50%) of the women in the U.S. The 50th percentile is also the same as the median of the population. The median value splits the population into two equal halves: one half that is below the median value, and one half that is above the median value. The number of people below the median value is the same as the number of people above the median value. If you are in the 50th percentile, that means you are above 50% of the population and below 50%. The 50th percentile is also called the median. What Does 75th Percentile Mean? The 75th percentile tells you the value that 75% of the population falls below. Alternatively, it is the value that 25% of the population is at or above. The 75th percentile is the top of the third quartile (Q3) of the population (a quartile is one-fourth). For example, the 75th percentile for the weight of U.S. women is 194.7 pounds. This means that a woman who weighs 194.7 pounds or less is in the bottom three quartiles (the bottom 75%) of the women in the U.S. If you are in the 75th percentile, that means you are above 75% of the population and below 25%. The 75th percentile is just below the bottom of the top quartile, Q4. What Does 95th Percentile Mean? The 95th percentile tells you the value that 95% of the population falls below. Alternatively, it is the value that 5% of the population is at or above. The 95th percentile is the value that puts you just below the top 5% of the population. For example, the 95th percentile for the weight of U.S. women is 263.0 pounds. This means that a woman who weighs 263.0 pounds or less is in the bottom 95% of the women in the U.S. What Does 99th Percentile Mean? The 99th percentile tells you the value that 99% of the population falls below. Alternatively, it is the value that 1% of the population is at or above. The 99th percentile is the value that puts you just below the top 1% of the population. For example, the 99th percentile for the weight of U.S. women is 303.1 pounds. This means that a woman who weighs 303.1 pounds or less is in the bottom 99% of the women in the U.S. How To Calculate Percentile To calculate percentile for a value X, take the following steps: List the data points in the population, ordered from smallest to largest.Count the total number of data points in the list (call this value N).Find out how many data points are below the value X (call this number B).Calculate the fraction 100B / N (the 100 in the percentile formula gives us a percentage).Round to the nearest integer (whole number with no fractions or decimals). Example 1: How To Calculate Percentile Let’s say that you take a test as one of 200 students. You get a 70 on the test. So, we want to calculate your percentile score for the 70 you got on the test. You can calculate your percentile compared to a group of test takers. After ordering the list of test scores from smallest to largest, we find that 174 of the data points are below a score of 70. So, this means: X = 70 (the value we want to find a percentile for)N = 200 (total number of data points in the list)B = 174 (number of data points below 70) Using the percentile score formula, we calculate: 100B / N=100(174) / 200=87 So, a score of X = 70 on the test puts you in the 87th percentile. That means your test score was higher than 87 percent of the other people who took the test. It also means that you are in the top 13 percent (100 – 87) of people who took the test. Example 2: How To Calculate Percentile Let’s say that you are in a group of 59 volunteers for a study. The researchers measure you height to be 71 inches. So, we want to calculate the percentile score for your 71 inch height (compared to the rest of the volunteers in the study). You can calculate percentile of height or weight based on a group of people. After ordering the list of heights from smallest to largest, we find that 47 of the data points are below a height of 71. So, this means: X = 71 (the value we want to find a percentile for)N = 59 (total number of data points in the list)B = 47 (number of data points below 71) Using the percentile score formula, we calculate: 100B / N=100(47) / 59=79.66 Rounding 79.66 up to 80, we find that a height of X = 71 puts you in the 80th percentile. That means you are taller than 80 percent of the other people who volunteered for the study. It also means that you are in the top 20 percent (top quintile, or one-fifth) for height of people who volunteered for the study. How To Find Rank From Percentile Sometimes, we want to work backwards and find the rank from the percentile. It is not always possible to get an exact number, but if we know the number of people in the group, we can get an idea of the rank based on a percentile. The general formula is: P / 100N where P is the percentile and N is the number of people in the population. Example: Find Rank From Percentile Let’s say that you are in the 48th percentile in a group of 158 test takers. This means P = 48 and N = 158. Using our formula to find rank from percentile, we get: NP / 100=158(48) / 100=75.84 Rounding 75.84 to 76, we find that your rank is around 76 (out of 158) on the test. So, you scored higher than 75 other test takers, and scored lower than 82 (158 – 76) test takers. Can Percentile Be More Than 100? Percentile cannot be more than 100. No matter what your score is on a test (or your height, or weight, etc.), your percentile cannot be higher than 100 percent. That is, you can score higher than everyone else in the population (putting you in the 99th percentile), but you cannot score higher than yourself (you cannot be in the 100th percentile or higher). Can Percentile Be Negative? Percentile cannot be negative. No matter what your score is on a test (or your height, or weight, etc.), your percentile cannot be lower than 0 percent. That is, you can score lower than everyone else in the population (putting you in the 0th percentile), but you cannot score lower than yourself. Can Percentiles Have Decimals? Percentiles are defined as integer values from 0 to 99 (so there are 100 of them). This means that a large population is split into 100 buckets of equal size. Keep in mind that for some population distributions with a “fat middle”, we can see multiple percentiles at the same value. For example, consider a fair 6-sided die with sides labeled 1, 2, 4, 4, 4, 4. In this case, the 50th, 75th, and 99th percentiles are all the value 4. If the percentile formula gives you a decimal or fraction, simply round to the nearest integer to get your percentile score. Is Percentile The Same As Z Score? A percentile is not the same as a z score (standard score), but they are related. For example, in a normal distribution, the 50th percentile is a z score of 0. A percentile is based on rank of a value in the population and number of people in the population. On the other hand, a z score uses the mean and standard deviation of a normal distribution to convert a value into a standard normal value. For example, let’s say we have a normally distributed population with a mean height of 70 inches and a standard deviation of 3 inches. Given a person with a height of 73 inches, we can calculate a z score and a percentile (which are not the same thing). To calculate the z score, we use the formula: Z = (X – M) / S where X is the height of the individual, M is the mean of the population, and S is the standard deviation. Here, we get: Z = (X – M) / SZ = (73 – 70) / 3Z = 3 / 3Z = 1 So, the z score for this person is 1. Using a standard normal table, we find that a z score of 1 corresponds to a percentile of 84. So, a person with a height of 73 is in the 84th percentile of this population (he is taller than 84 percent of people, and is the top 16 percent for height). Conclusion Now you know how to interpret percentile and how it relates to z scores. You also know how to calculate percentiles and ranks from population data. I hope you found this article helpful. If so, please share it with someone who can use the information. Don’t forget to subscribe to my YouTube channel & get updates on new math videos! ~Jonathon