Answer :
Final answer:
To find the 20th and 80th percentiles, the data is first sorted in ascending order. The percentile rank is then calculated, and if it's not an integer, interpolation is used. In this set, the 20th percentile is 170.8 and the 80th percentile is 187.6.
Explanation:
Calculating percentiles involves first sorting your data in ascending order. The formula to find the rank (position in the sorted list) of the percentile is: Pth percentile Rank = (P/100)(N+1), where P is the desired percentile (in this case 20 or 80), and N is the number of data values.
Once you have the rank, if it's an integer, the value at that rank is the percentile. If it's not an integer, you determine the percentiles by interpolation, i.e. find the two integers it is between, and then interpolate based on the fractional part.
Let's demonstrate this with the given set with 10 values. We sort them in ascending order: 168, 170, 174, 176, 180, 182, 186, 186, 188, 198.
To find the 20th percentile, we use: Pth percentile Rank = (20/100)(10+1) = 2.2. Since this is not a whole number, the value of the 20th percentile is between the second and third value in our array (which are 170 and 174 respectively). Performing linear interpolation, the 20th percentile is 170 + 0.2 * (174 - 170) = 170.8.
To find the 80th percentile, we use: Pth percentile Rank = (80/100)(10+1) = 8.8. The rank then falls between the 8th and 9th value in the array (186 and 188). Performing linear interpolation, the 80th percentile is 186 + 0.8 * (188 - 186) = 187.6.
Learn more about Percentiles here:
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