Interpolation : Interpolation Interpolation : Interpolation Interpolation provides a way to find values that do not appear directly on the table itself
95th percentile= 4.5, x=3.5 = 70%
But….. Interpolation : Interpolation What is the 50th percentile?
What is the percentile rank for x=4? This is where interpolation comes in The Interpolation Process : The Interpolation Process A single interval is measured on two different scales (time and distance for instance) – the endpoints are known for each scale
You are given an intermediate value on one of the scales, the problem is to find the corresponding intermediate value on the other scale
Find the width of the interval on both scales
Locate the position of the intermediate value in the interval. This position corresponds to a fraction of the whole interval
The fraction = the distance from the top of the interval over the interval width
Use this fraction to determine the distance from the top of the interval on the scale
Distance = (fraction) X (width)
Use the distance from the top to determine the position on the other scale The Interpolation Process as it is in my head : The Interpolation Process as it is in my head You are looking to determine the the distance from the top on the scale that you do know so that you can apply it to the scale that you do not have the value for, but to do this you have to convert the values proportionately Now, on to an example! : Now, on to an example! Learning Check, p58 : Learning Check, p58 40th percentile?
Width = 10 (x column)
= 40 (60%-20%)
29.5 = 60 (remember real limits)
? = 40
19.5 = 20 So, 40 is 20 from the top of the interval that we know (60-40=20)
Take 20 and place it over the total = 20/40 = ½
Now you have to apply this to the other width, which is on a different scale, but since
we know it these numbers proportionately we are in good shape
½ (from above) times 10 (the width of x) = 10/2 = 5
Therefore, the answer is 5 from the top of the x interval or 24.5 Learning Check p58 cont. : Learning Check p58 cont. X= 32? #21 : #21 Find X=5, X=12, the 30th percentile and the 72nd percentile.