Question

STATISTICS: The interquartile range is given by
IQR = Q3 - Q1, where Q1 is the lower quartile, and it falls above 25% of the data, and Q3 is the upper quartile, and this falls above 75% of the data

To get the quartiles, the easy way is to find the median, and then split the data like that

For example, we have the values:
-17.5, 2.8, 3.2, 13.9, 14.1, 25.3, 45.8

The median is 13.9

Now, we split up the data into two halves from this number, and when the median is odd, we include the median in both halves:
(see next post for question)

Answer 1

lower half: -17.5, 2.8, 3.2, 13.9
upper half: 13.9, 14.1, 25.3, 45.8

So then, we get the median of the data (ex. lower half) and we will get the quartile (Ex. if we get the median for the lower half of the data, we get the Q1, or lower quartile, or the 25th percentile)

My question is: How would I get the 10th percentile, which is the number that falls above 10% of the data values?

Answer 2

How do you know where is the number above 10% of the data values?

Answer 3

Also, can this be done by hand?

Answer 4

This is what I got from Stanford.

Formula: \[i= (np/100)+0.5\]
where i is rank of the desired percentile
n is the number of data values
P is the percentile

If i is an integer, xi is simply the pth percentile.
If i is not an integer, interpolate as follows:
let k = the integer part of i
let f = the fractional part of i
(i.e., if k = 10.375, then k = 10 and f = 0.375)
let xint = the value we want to interpolate between \[x _{k} and x _{k+1}\]:
xint= \[(1-f)_{x _{k}}+f _{x _{k+1}}\]

Given this data: -17.5, 2.8, 3.2, 13.9, 13.9, 14.1, 25.3, 45.8

i=(10x10/100)+0.5=1.05
Since i is not an integer, you'll have to interpolate.
k=1; f=0.05
xint=(1-0.05)(-17.5)+(0.05)(2.8)= -16.485