TYPES OF DATA

Presented by Hnin Thiri Chaw (9PhD-3)

OUTLINE

What is Statistics ? Type of Statistics Type of Sampling Four Level of Measurement Describing Data: Frequency Distributions and

Graphic Presentation

WHAT IS STATISTICS?

The science of collecting, organizing, presenting, analyzing and interpreting data to assist in making more effective decision.

TO MAKE IMPORTANT DECISION

Determine existing information and additional information.

Gather additional information, but does not lead misleading result.

Summarize information in a useful and informative manner.

Analyze the available information. Draw conclusion while assessing the risk and

incorrect conclusion

TYPE OF STATISTICS

Descriptive Statistics(Without analysis) Method of organizing, summarizing and

presenting data in an informative way. Inferential Statistics(With analysis)

Population(A collection of all possible individuals, objects, or measurements of interest.)

Sample (A portion, or part of the population of interest)

SAMPLING A POPULATION

Reason Impossible to check or locate all the members of

the population Cost of Studying all the items in the population

may be prohabitive. The result of a sample is the estimate of the

population parameter thus saving time and money.

It may be too time consuming to contact all the members of the population.

TYPE OF SAMPLEType of Sample

Probability Sample

Simple Random Sampling

Systematic Sampling

Stratified Sampling

Cluster Sampling

Non Probability Sample

Panel Sampling

Convenience Sampling

PROBABILITY SAMPLE

Simple Random Sample all members of the population has the same

chance of being selected for a sample. Systematic Sample

A random starting point is selected, then every k item is selected for the sample.

Stratified Sample Population is divided into several groups or

strata and then a sample is selected from each stratum.

Cluster Sample Primary units and then samples are drawn from

the primary unit.

NONPROBABILITY SAMPLING

Inclusion in the sample is based on the judgment of the person conducting the sample.

Non Probability samples may lead to biased result.

SAMPLING ERROR

The difference between the population parameter and the sample statistic are called the sampling error.

TYPE OF VARIABLE

Data

Qualitative

ExampleType of car owned

Color of PenGender

Quantitative or numerical

Discrete

Number of Children

Number of EmployeeNumber of

TV Set Sold last

year

Continuous

Weight of a

shipmentMiles driven

Distance Between New York

and Bankok

QUALITATIVE VARIABLE

Gender, Religious Affiliation, Type of automobile owned, State of Birth , Eye color

Qualitative variable can be summarized in bar chart or pie chart.

For example What percentage of population has blue eye? How many Buddhist and Catholics in Myanmar? What percent of the total number of car sold last

month were Toyota?

QUANTITATIVE VARIABLE

Discrete (Gaps between possible values) or Continuous (Any value within specific range)

Discrete variable result from counting ( there is no 3.56 room in a house) Example of Discrete variables

number of bedrooms in a house(1, 2,3,4 etc) number of car arrive toll booth(4, 1, 2 etc) number of student in each section.

QUANTITATIVE VARIABLE

Continuous variable can result from measuring something.

Example of Quantitative Variable Air pressure in a tire (15.1 ,15.4, 15.0) The amount of raison in a box (8g, 8.4, 8.2g) Time taken of a flight(Ygn to mdy -> 2hours,

2hour 20 minutes, 2 hour 10 minutes) depend on the accuracy of time device

SOURCE OF STATISTICAL DATA

Secondary Data ( Government publication, Statistical year book, Published Data)

FOUR LEVEL OF MEASUREMENT Nominal Level Data

- Data are sorted into categories with no particular order to the categories.* Mutually Exclusive- An individual object can appear in one category.*Exhaustive- An individual object appear in at least one of the categories.

Ordinal Leval Data One Category is ranked higher than the other

Interval Level Data- Ranking characteristic of Ordinal + Distance between value is meaningful

Ratio Level Data all characteristic of interval +zero pt and the ratio of two value is meaningful

NORMINAL LEVEL DATA

Carrier Number of calls PercentAT&T 108115800 75MCI 20577310 14Sprint 8238740 6Other 7130620 5

Total 100%

ORDINAL LEVEL DATA

Rating of a finance professorRating FrequencySuperior 6Good 28Average 25Poor 12Inferior 3

INTERVAL LEVEL DATA

Temperature( can count , classified, can add, subtract)

Note : zero degree Fahrenheit does not represent absence of heat.

RATIO LEVEL DATA

Point zero is meaningful. The ratio of two values is also meaningful. Example-wage, unit of production, weight,

height.Income

Name Father SonJone $ 80000 40000White 90000 30000Rho 60000 120000Scazzro 750000 130000

HOW TO DISTINGUISH BETWEEN FOUR LEVEL OF DATA

Norminal

Ordinal Interval Ratio

Mutual Exclusive(in one category)

* * * *

Can be presented in Percentage

* * * *

Ranking Order * * *

Meaningful Interval

* *

Addition & Subtraction

* *

Meaningful Zero *

Meaningful Ratio

*

Can Multiply & Divide

*

WHAT IS THE LEVEL OF MEASUREMENT FOR EACH OF THE VARIABLE?

Student Grade point Average

?

Ans: Interval

WHAT IS THE LEVEL OF MEASUREMENT FOR EACH OF THE VARIABLE?

Ranking of Student by freshmen, junior , senior

?

Ans: Ordinal

WHAT IS THE LEVEL OF MEASUREMENT FOR EACH OF THE VARIABLE?

Number of hours Student Study per week

?

Ans: Ratio

DESCRIBING DATA: FREQUENCY DISTRIBUTION AND GRAPHIC PRESENTATION

A frequency distribution is a grouping of data into categories showing the number of observation in each mutually exclusive category.

The steps in constructing a frequency distribution are: 1 .Decide on the size of the class interval. 2. Tally the raw data into the classes. 3. Count the number of tallies in each class.

CLASS FREQUENCY &CLASS INTERVAL

The class frequency is the number of observation in each class.

Class Interval => i= Highest Value – Lowest Value/number of Class Class interval is the difference between the lower

limit of the two consecutive classes. Class mid point is the halfway between the lower

limit of two consecutive classes.

CRITERIA FOR CONSTRUCTION FREQUENCY DISTRIBUTION

Avoid having fewer than 5 or more than 15 classes.

Avoid Open ended Class. Keep the class interval same size. Do not have overlapping classes.

RELATIVE FREQUENCY

The relative fequency distribution shows the percent of the observation in each class.

There are two method for graphically portraying frequency distribution.

1. Histogram=> portrays the number of frequencies in each class in the form of rectangle.

2. Frequency Polygon=> line segment connecting the point formed by the intersection of the class mid point and the class frequency.

ANOTHER ALTERNATIVE

Line Chart => ideal for showing the trend of sale, income over time.

Bar Chart => showing the changes in business and economic data over time.

Pie Chart => the percent of various components are of total.

CASE STUDYTABLE-SELLING PRICE OF VEHICLES SOLD LAST MONTH AT WHITNER PONTIAC

$20197

20372 17454 20591 23651 24453 14266 15021 25683 27872

16587 20169 32851 16251 17047 21285 21324 21609 25670 12546

12925 16873 22251 22277 25034 21533 24443 16889 17044 14357

17155 16688 20657 23613 17895 17203 20765 22783 23661 29277

17642 18981 21052 22799 12754 15263 33625

14399 14968 17356

18442 18722 16331 19817 16766 17633 17962 19845 23285 24896

26076 29492 15890 18740 19374 21571 22449 25337 17642 20613

21220 27655 19442 14891 17818 23237 17455 18556 18639 21296

Lowest

Highest

Total Frequencies =80

CALCULATING CLASS INTERVAL(1)

i=High Value-Low Value/Number of Classes i=(33625-12546)/8=$ 2635(suggested class

interval) $2635 is awkward to work with and difficult

to tally. We round up the $2635 , Say $ 3000

CALCULATING THE CLASS INTERVAL BASE ON THE NUMBER OF OBSERVATIONS(2)

i=(High Value – Low Value)/1+3.322*log of total frequencies

i=($33625-$12546)/1+3.222(Log 10

80 )=$2879 Rather than the awkward value,nearby value

$ 3000 is easier.

FREQUENCY DISTRIBUTION OF SELLING PRICE AT WHITNER PONTIAC LAST MONTH

Selling Prices ( $ thousands)

Frequency Relative Frequency

12 up to 15 8 8/80=0.1000

15 up to 18 23 0.2875

18 up to 21 17 0.2185

21 up to 24 18 0.2250

24 up to 27 8 0.1000

27 up to 30 4 0.0500

30 up to 33 1 0.0125

33 up to 36 1 0.0125

Total 80 1

NOW THAT WE HAVE ORGANIZED THE DATA INTO A FREQUENCY DISTRIBUTION, WE CAN SUMMARIZE THE SELLING PRICES OF THE VEHICLES FOR ROB WHITNER Selling Price ranged from about $12000 up to

about $36000. Selling price are concentrated between $15000

and $ 24000. A total of 58, or 72.5 percent of vehicles sold

within this range. The largest concentration is in $15000 up to

18000 class. The middle of the class(mode) is $16500 , so

the typical selling price is 165000. By presenting the information to the Mr.

Whitner , we give him a clear picture of the distribution of selling prices for last month.

FREQUENCY POLYGON

2 Frequency Mid Point

12 up to 15 8 13.5

15 up to 18 23 16.5

18 up to 21 17 19.5

21 up to 24 18 22.5

24 up to 27 8 25.5

27 up to 30 4 28.5

30 up to 33 1 31.5

33 up to 36 1 34.5

Total 80

Reference

Statistical Techniques in business and economics

Author : Robert D. MasonDouglas A. LindWilliam G. Marchal

“SHARING IS CARING”THANKS FOR YOUR ATTENTION!