1. MATH 201: STATISTICS Chapters 1 & 2 : Elements of Statistics
Methods for Describing Sets of Data

2. Statistics Is the science of data that involves
collecting
classifying, summarizing, organizing (describing!)
analyzing and interpreting (making inference!)
numerical information (DATA)
Descriptive statistics
Numerical and Graphical methods to look for patterns in a data set, to summarize the information and present it in a convenient form.
Inferential statistics
Utilizes sample data to make estimates, decisions, predictions or other generalizations about the population.

3. In short, activities subsumed under statistics:
Data collection.
Presenting, summarizing, and interpreting data (data analysis).
Drawing conclusions and generalisations (inference).
Best learned by practising it...

4. Population and Sample
A population is a set of units (usually people, objects, items) that we are interested in studying.
A sample is a subset of the units of a population.
OR,
Population: the set of measurements corresponding to the entire collection of units under study.
Sample: the set of measurements that are actually collected in the course of an investigation.

5. Random sample
A random sample of n units is a sample selected from the population in such a way that every different sample of size n has the same chance to be selected.
A random sample is representative of the population, that is it exhibits characteristics typical to the target population.
In most studies, it is difficult to obtain information from the entire population. We rely on samples to make estimates or inferences related to the population.

6. What is a variable?
A variable is a characteristic or property of an individual population unit.
It can have different values which
vary from person to person, item to item, etc.
A value is a number or cathegory
Quantitative data are measurements that are numerical naturally.
Qualitative data are measurements that are not themselves numbers, but can be classified as one of several categories.

7. Population and Census Data
Identifier
Color
MPG
RD1
Red 12
RD2 10
RD3 13
RD4
RD5
BL1
Blue 27
BL2 24
GR1
Green 35
GR2
GY1
Gray 15
GY2 18
GY3 17 11 14

8. Sample and Sample Data Identifier Color MPG RD2 Red 10 RD5 13 GR1
Green 35
GY2
Gray 18 15

9. What are the variables? Identifier? Color? MPG (miles per gallon)?
Are the data qualitative or quantitative? Which variable is which?
ANSWERS:
Identifier is just the name of each individual unit in the population.
Color is a qualitative variable
MPG is a quantitative variable

10. Population Examples Variable vs Population
Employment status - Status of ALL employable people (employed, unemployed) in Turkey.
Quantitative ÖSS Scores – Quantitative ÖSS score of EVERY person that took the ÖSS during 2004
The condition of having coffee or not - Responses of ALL currently enrolled college (university) students as to whether they have had coffee in the morning (Yes or No)
values

11. 2-1 Describing Qualitative Data
Class frequency: Number of observations in the data set that falls into a particular class (cathegory).
Relative frequency: class freq. / n
it may also be written as percentage
A pie chart is convenient for qualitative data
Draw a pie chart for the “cars” example

12. 2-2 Describing Quantitative Data
Dot Plots
Stem and Leaf Display
Histogram
Mileage Ratings on 100 cars (MPG)