1. Friday, October 2
Variability

2. CENTRAL TENDENCY
Mode
Median
Mean
nominal
ordinal
interval

3. Variability CENTRAL TENDENCY Mode Median Mean nominal ordinal interval
Range
Interquartile Range
“Then there is the man who drowned crossing a stream with an average depth of six inches.” - W.I.E. Gates
interval
Variance
Standard Deviation

5. Range

6. Box Plot
Interquartile
Range
Range

7. _ X

8. The population mean is µ. The sample mean is X._ _
The population mean is µ. The sample mean is X.

9. s Population µ  _ X _ The population mean is µ. The sample mean is X.
The population standard deviation is , the sample sd is s.

10. SS 2 N Variance of a population, 2 (sigma squared).
It is the sum of squares divided (SS) by N SS 2 = N

11. SS  (X –  ) 2 N Variance of a population, 2 (sigma squared).
It is the sum of squares divided (SS) by N
 (X –  ) 2 SS 2 = N

12. SS  N The Standard Deviation of a population, 
It is the square root of the variance. SS  = N
This enables the variability to be expressed in the same unit of measurement
as the individual scores and the mean.

13. The population mean is µ. The sample mean is X._ _
The population mean is µ. The sample mean is X.

14. s Population µ  _ X _ The population mean is µ. The sample mean is X.
The population standard deviation is , the sample sd is s.

15. In reality, the sample mean is just one of many possible sample
SampleC XC _
SampleD XD _
Population
SampleB XB _
SampleE XE
SampleA XA _ _
In reality, the sample mean is just one of many possible sample
means drawn from the population, and is rarely equal to µ.

16. In reality, the sample mean is just one of many possible sample
SampleC XC _
SampleD XD sc _ sd
Population
SampleB XB _  sb
SampleE XE
SampleA XA _ _ se sa
In reality, the sample mean is just one of many possible sample
means drawn from the population, and is rarely equal to µ.

17. Sampling error = Statistic - Parameter_
Sampling error for the mean = X - µ
Sampling error for the standard deviation = s - 

18. Unbiased and Biased Estimates
An unbiased estimate is one for which the mean sampling
error is 0. An unbiased statistic tends to be neither larger
nor smaller, on the average, than the parameter it estimates.
The mean X is an unbiased estimate of µ.
The estimates for the variance s2 and standard deviation s
have denominators of N-1 (rather than N) in order to be
unbiased. _

19. SS 2 = N

20. SS s2 =
(N - 1)

21. _
 (X – X ) 2 SS s2 =
(N - 1)

22. SS
(N - 1) s =

23. Computational formula
Conceptual formula VS
Computational formula

24. What is a measure of variability good for?