Find and interpret the percentile of an individual value in a distribution of data.
Percentile is percent. Find the percent to get percentile. If they are in the xth percentile, they have a higher or equal value than x percent of the sample.
Percentile is a measure that indicates the position of a value in a data distribution relative to all other values. It is denoted by the value ‘P’ and ranges from 0 to 100.
To find the percentile of an individual value in a distribution of data, we need to follow the steps below:
Step1: Sort the data in ascending or descending order from lowest to highest or vice-versa.
Step 2: Count the number of values in the data set, denoted by ‘n’.
Step 3: Use the formula below to calculate the percentile of the individual value ‘X’ in the data set.
Percentile (P) = (number of values below X / n) * 100
For example, if we have a distribution of test scores in a class as follows: 40, 50, 60, 70, 80, 90 and we want to know the percentile of a score of 70. First, we sort the test scores in order: 40, 50, 60, 70, 80, 90. There are 6 values in the data set (n=6). Since 70 is larger than 3 values (less than 80, 90, 80), we count the number of values below it (3), then apply the formula:
Percentile (P) = (number of values below X / n) * 100
= (3/6) * 100
= 50
Therefore, the percentile of a score of 70 in the class is 50, indicating that 50% of the scores in the class are lower than this score and 50% are higher.
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