1. DESCRIPTIVE STATISTICS BORAM KANG

2. STATISTICS
The only science that enables different experts using the same figures to draw different conclusions.
Evan Esar ( ), US humorist

3. 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

4. DATA Values along with their context
The data we collect can be represented on one of FOUR types of scales:
Nominal
Ordinal
Interval
Ratio

5. NOMINAL SCALE Describe something by giving it a name. For example:
Numbers are Names
Describe something by giving it a name. For example:
Question ! Female or Male ?
Gender: 1 = Female, 2 = Male

6. 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

7. 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°

8. 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

9. 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

10. So, how much do the actual scores deviate from the mean?
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

11. MEAN – “SEE SAW” (FROM TAL, 2001)

12. SHAPES OF DISTRIBUTIONS

13. EXAMPLE
I asked 12 people how many cars they had owned in their lives. Here are the answers I got:

14. What’s the mode of this distribution? 3, 8 Median? 5.5 Mean? 5.5
<1,2,3,3,4,5,6,7,8,8,9,10>
Histogram 1 4 6 5 7 8 9 2 3
frequency
# of cars ever owned 10
What is the value of “N”? 12
What’s the mode of this distribution? 3, 8
Median?
Mean?
Range?
IQR? <1,2,3,3,4,5,6,7,8,8,9,10>
8-3=5
Standard Deviation?2.81

15. 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).

16. CITATION
hill.com/sites/ /student_view0/statistic s_primer.html
deviation.php
chProcess/IntervalScale.htm