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 represents the position of an individual value in a distribution of data relative to other values. It indicates the percentage of data values that are equal to or less than the individual value. To calculate the percentile of an individual value in a distribution of data, follow the steps below:
1. Rank the data set values from lowest to highest.
2. Calculate the total number of values in the data set (n).
3. Compute the rank of the individual value using the formula:
rank = (number of values less than the individual value) + 0.5(number of values equal to the individual value)
4. Divide the rank by the total number of values (n) and multiply by 100 to obtain the percentile.
For example, suppose we have the following data set: 5, 7, 8, 10, 12, 13, 15, 17, 19, 20 and we want to find the percentile of the value 13. Using the above formula, we obtain:
– Rank of 13 = (5 values less than 13) + 0.5(1 value equal to 13) = 5.5
– Percentile of 13 = (5.5/10) x 100 = 55
Therefore, the 13th value in the data set is at 55th percentile, which means that 55% of the data values are equal to or less than 13.
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