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Session 2 Handout
Clarification of Some Common Misconceptions
•
Mean, median, variance and other descriptive statistics are NOT exclusive to the normal
distribution.
•
The normal distribution is a case of symmetrical distribution in which theoretically,
mean=median
•
“(Empirical) distribution” aka sampling distribution, means where the data points are;
theoretical distribution means where the data points “should be”.
•
In empirical distributions, mean & median rarely exactly equal, so whereas it cannot be PROVED
that a set of data points is normally distributed, it can be shown that the set of data points is not
too deviant from the (theoretical) normal distribution.
•
Descriptive statistics of a sample are conceptually and computationally different from
descriptive statistics of a population, ie the sample mean is defined and calculated differently
from population mean, the sample variance is defined and calculated differently from
population variance, and so on.
Demo – Mean & Median
http://opl.apa.org/contributions/Rice/rvls_sim/stat_sim/descriptive/index.html
Descriptive Statistics Exercise
•
Suppose a waitress recorded the amount of tips she got from a few tables at a birthday party.
Calculate & interpret the following statistics:
Sample Median, Sample Mean, Sample Variance, Sample Standard Deviation
Data Set
Index
A
Data points (ie Sample)
17, 15, 23, 7, 9, 13, 39, 5
Sample
median
14
Sample
mean ( )
16
Sample
2
variance (s )
120
Sample standard
deviation (s)
≈10.95445
B
18, 16, 24, 8, 10, 14, 40, 6
15
17
120
≈10.95445
C
19, 17, 25, 9, 11, 15, 41, 7
16
18
120
≈10.95445
D
20, 18, 26, 10, 12, 16, 42, 8
17
19
120
≈10.95445
In this exercise, all data points were systematically increased by 1 unit across data sets, hence only
sample medians and sample means changed. In general, if the sample distribution only shifts location
across samples and the relative distances between data points within the sample do not change (ie the
change of data points between samples is systematic), then only the sample median and sample mean
change; Measures of within-sample variability (sample variance and sample standard deviation) do not
change, as the within-sample relative distances between individual data points with respect to the
sample mean do not change.