DESCRIPTIVE STATISTICS
BORAM KANG
STATISTICS

The only science that enables different experts
using the same figures to draw different
conclusions.

Evan Esar (1899 - 1995), US humorist
STATISTICS(SINGULAR)
AND STATISTICS(PLURAL)
A way of reasoning, a long with a collection of tools
and methods, designed to help us understand the
world.
Calculations made from data
DATA


Values along with their context
The data we collect can be represented on one of
FOUR types of scales:
Nominal
 Ordinal
 Interval
 Ratio

NOMINAL SCALE

Numbers are Names
 Describe
something by giving it a name.
For example:
 Question

! Female or Male ?
Gender: 1 = Female, 2 = Male
ORDINAL SCALE
An ordered set of objects.
 But no implication about the relative SIZE of the
steps.


•
Questions ! How do you feel about this?
Good / Medium/ Bad
INTERVAL SCALE
 Ordered,
like an ordinal scale.
 Plus there are equal intervals between
each pair of scores.
 Questions ! Temperature (Fahrenheit)
•
•
100° is 10° warmer than 90°(+ -)
But We can’t say (* /)
-100° is not twice as warm as 50°
RATIO SCALE
Interval scale, plus an absolute zero.
 Sample:



•
Distance, weight, height, time (but not years – e.g.,
the year 2002 isn’t “twice” 1001).
Questions! Age
30 years old/ 15 years old : twice
MEASURES OF CENTRAL
TENDENCY

Mode


Most frequent score (or scores – a distribution can
have multiple modes)
Median
“Middle score”
 50th percentile


Mean - µ (“mu”)
“Arithmetic average”
 ΣX/N


Range




Max-Min
So, how much do the actual scores deviate from
the mean?
We need <the Standard Deviation >
Add up all the deviations and we should have a
feel for how disperse, how spread, how deviant,
our distribution is. That’s the Standard Deviation
MEAN – “SEE SAW” (FROM TAL, 2001)
SHAPES OF DISTRIBUTIONS
EXAMPLE
I asked 12 people how many cars they had owned in their lives. Here are
the answers I got:
10
1
4
8
8
2
3
6
3
5
9
7
<1,2,3,3,4,5,6,7,8,8,9,10>
Histogram
frequency
3
2
1
1
2
3
4
5
6
7
8
# of cars ever owned
What is the value of “N”?
12
What’s the mode of this distribution?
3, 8
Median?
5.5
Mean?
5.5
Range?
10-1
9
IQR? <1,2,3,3,4,5,6,7,8,8,9,10>
8-3=5
Standard Deviation?2.81
9
10
SO WHICH DO WE USE?

It depends on:
 The type of scale of your data
 Can’t use means with nominal or ordinal scale
data(female/male) (good/middle/bad)
 With nominal data, must use mode
 The distribution of your data
 Tend to use medians with distributions bounded at
one end but not the other (e.g., salary).
 The question you want to answer
 “Most popular score” vs. “middle score” vs. “middle of
the see-saw”
 “Statistics can tell us which measures are technically
correct. It cannot tell us which are ‘meaningful’” (Tal,
2001, p. 52).
CITATION
http://highered.mcgrawhill.com/sites/0072494468/student_view0/statistic
s_primer.html
 http://easycalculation.com/statistics/standarddeviation.php
 http://www.uoguelph.ca/htm/MJResearch/Resear
chProcess/IntervalScale.htm
