This document provides an overview of key statistical concepts including: 1. The average (arithmetic mean) is calculated by summing all values and dividing by the number of samples. 2. The median is the middle value of a data set when values are sorted from lowest to highest. 3. The 90th percentile represents the value where 90% of values are below it. 4. Standard deviation measures how spread out values are from the average and 68% of values fall within one standard deviation of the average in a normal distribution.

1. Statistics for Dummies
Fred Moyer
@phredmoyer
@circonus

2. Data
“Without data, you’re just another person
with an opinion”
W. Edwards Deming

3. Average
“Arithmetic Mean”
Avg = sum / # samples
avg(1,2,3) = 6/3 = 2

4. Median
Midpoint of a data set
50th percentile q(0.5) = 33
Value 11 22 33 44 55
Sample 1 2 3 4 5

5. 90th Percentile
90% of the values are below it
q(0.9) = 100
Value 11 22 33 44 55 66 77 88 99
100 111
Sample 1 2 3 4 5 6 7 8 9 10 11

6. Histogram
Sample Value
Number of
Samples

7. Normal Distribution
Sample Value
Number of
Samples
Median = Mode = Average

8. Standard Deviation
Sample Value
Number of
Samples
68.1% of values within one
sigma (standard deviation)

9. Standard Deviation (σ)
Subtract the mean μ from all the samples, square the
difference, sum and divide by number of samples

10. Non Normal Distribution
Sample Value
Number of
Samples

11. Non Normal Distribution
Sample Value
Number of
Samples
Median
Mode
What’s the
standard
deviation?

12. Percentiles
Sample set A q(0.95) = 10
Sample set B q(0.95) = 20
What is q(0.95) for A U B?

13. Percentiles
a(0.95){A U B} !=
avg( q(0.95){A} + q(0.95){B} )
q(0.95){A U B } needs raw data

14. Null Hypothesis
“The Double” = 2012
Determine who is Cassius the Assassin

15. Null Hypothesis
“Stephen Hawking is Cassius”
Formulate a null hypothesis
“Stephen Hawking is not Cassius”

16. Null Hypothesis
Try to disprove the null hypothesis
Hawking wasn’t in any crime scene photos
Null hypothesis proved, Hawking != Cassius
Large p-value, > 0.05, weak evidence against

17. Null Hypothesis
“Richard Gere is Cassius”
Formulate a null hypothesis
“Richard Gere is not Cassius”

18. Null Hypothesis
Try to disprove null hypothesis
Richard Gere was in ALL of the crime
scene photos
Small p-value, <= 0.05, weak evidence for

19. Null Hypothesis
Null hypothesis disproved
Richard Gere is Cassius

20. Don’t be a Dummy
Go learn some statistics!