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Statistics 101

Introduction
Quartiles
Percentiles
6. Percentiles – computing methods
Quantiles
Standard Deviation and Variance

Instruction

Find the percentiles of this set:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ... , 99, 100

There are 100 elements in this set. Using the formula \lceil\frac{p}{100}n\rceil we get the results:

Percentile p Position Percentile value
5^\text{th} \lceil\frac{5}{100}100\rceil=5 5
25^\text{th} \lceil\frac{25}{100}100\rceil=25 25
50^\text{th} \lceil\frac{50}{100}100\rceil=50 50
70^\text{th} \lceil\frac{70}{100}100\rceil=70 70
75^\text{th} \lceil\frac{75}{100}100\rceil=75 75

Let's try a smaller set:

1, 4, 6, 8, 10, 12, 14, 16, 18, 20

And calculate a few percentiles:

Percentile p Position Percentile value
5^\text{th} \lceil\frac{5}{100}10\rceil=\lceil0.5\rceil=1 1
25^\text{th} \lceil\frac{25}{100}10\rceil=\lceil2.5\rceil=3 6
50^\text{th} \lceil\frac{50}{100}10\rceil=\lceil5\rceil=5 10
65^\text{th} \lceil\frac{65}{100}10\rceil=\lceil6.5\rceil=7 14
70^\text{th} \lceil\frac{70}{100}10\rceil=\lceil7\rceil=7 14
75^\text{th} \lceil\frac{75}{100}10\rceil=\lceil7.5\rceil=8 16