Statistics Fundamentals: Measures of Location

The following are a few distribution divisions’ breakdowns: (i) Quartiles into quarters, (ii) quintiles into fifth, (iii) percentiles into hundredths.
 
Measuring the location and potential data can be done through simple arithmetic and in some circumstantial situations, interpolation (linear). Interpolation is another way of saying estimating a missing value.
 
The Basic Formula: Py will refer to the Xvalue at or below the yth percentile in ascending order

• Py = Ly = (n +1) * (y/100), where (i) n is the number of observations and (ii) y is the percentile.; If Ly is a whole number then the Xvalue of the Ly would equal Py
• For instance we have the following data set: 2, 4, 7, 9, 11. We want to look for the 50th percentile. Therefore we will do the following: (i) Ly = (5 + 1) * (50/100) = 3; (ii) answer will then be 7 as it is the 3rd number in ascending order

If Ly is not a whole number, then we must use linear interpolation, which means estimating an unknown value on the basis of two known values that surround it:

• Linear Interpolation Example: Py = Xvalue of LyLower + (Ly – LyLower) * (Xvalue of LyUpper – Xvalue of LyLower).For instance we have the following data set: 2, 4, 7, 9, and 11. We want to look for the 70th percentile. Therefore we will do the following:
  • Ly = (5 + 1) * (70/100) = 4.2;
  • Therefore, the number “9” is the 4th value in ascending order, where the formula is (4.2 – 4) * (11 - 9) = 9.4