intro of statistics - ogive

7/30/2019 Intro of Statistics - Ogive

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STATI ST ICA L A NA LYSIS

(FP531)


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CHAPTER 1

BAS IC STATI ST IC S

1.1 UND ERSTAND

STATISTICS


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ST AT IST IC D E F INIT ION

Statistics is the branch of science which

deals with the collection, classification and

tabulation of numerical facts as the basis forexplanations, description and comparison of

Phenomenon


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Phenomenon


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Phenomenon


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T W O T YP E S O F STAT I ST I C

DESCRIPTIVE INFERENTIAL


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DESCRIPTIVE STATISTICS

Descriptive statistics are used to summarizethe characteristics of a data set


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INFERENTIAL STATISTICS

Use data gathered from a sample to make

inferences about the larger population fromwhich the sample was drawn. Allows the

formation of conclusions about almost any

parameter from a sample takenfrom a larger population


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Population versus Sample

The entire group of individuals about which we

seek information. Such as the height ofevery person in the PUO, or the volume of every

HALAGEL toothpaste that a manufacturerproduces

S Part of the population from which we actually

collect information. Such as the volumes of thelast thirty HALAGEL toothpaste


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Types of variables

QUANTITATIVE QUALITATIVE


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QUANTITAVE VARIABLE

A quantitative variable is naturally measured

as a number for which meaningful arithmeticoperations make sense. Examples: Height,

age, crop yield, GPA, salary, temperature,

area and air pollution index


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QUALITATIVE VARIABLE

Qualitative/Categorical variables take a

value that is one of several possible

categories. As naturally measured,qualitative variables have no numerical

meaning. Examples: Hair color, gender, field

of study, college attended,, status of diseaseinfection


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SCALES OF MEASUREMENT

Scales of measurement refer to ways in

which variables/numbers are defined and

categorized. The four scales of measurementare nominal, ordinal, interval, and ratio.


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MEASUREMENT: NOMINAL

Nominal numbers are simply numbers thatare different. 1 is not 2. 3 is not 9. It really

makes more sense to think of things like

apples and oranges. We just assign numbersto things because it makes doing statistics

and creating charts easier.


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MEASUREMENT: ORDINAL

Ordinal refers to quantities that have anatural ordering. The ranking of favorite

sports, the order of people's place in a line,

the order of runners finishing a race or moreoften the choice on a rating scale from 1 to

5. (Likert questions).


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MEASUREMENT: INTERVAL

Interval data is like ordinal except we can saythe intervals between each value are equally

split. Example, temperature in degrees

Fahrenheit. The difference between 29 and30 degrees is the same magnitude as the

difference between 78 and 79.


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MEASUREMENT: RATIO

The weight of an object would be anexample of a ratio scale. Weights can be rank

ordered, units along the weight scale are

equal to one another, and there is anabsolute zero. Due to the presence of a zero,

it now makes sense to compare the ratios of

measurements. Phrases such as "four times"and "twice" are meaningful at the ratio level.


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DIFFERENCES OF MEASUREMENT

MEASUREMENT DIFFERENCE DIRECTION OFDIFFERENCE

AMOUNT OFDIFFERENCE

ABSOLUTEZERO

Nominal X

Ordinal X X

Interval X X X

Ratio X X X X


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CHAPTER 1

BAS IC STATI ST IC S

1. 2 OR GA NI ZE DATA


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RAW DATA

Raw data (sometimes called source data oratomic data) is data that has not been

processed for use. A distinction is sometimes

made between data and information to theeffect that information is the end product of

data processing. Raw data that has

undergone processing sometimes referred toas cooked data
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FREQUENCY DISTRIBUTION

The convenient method of organizing data isto construct a frequency distribution. A

frequency distribution table is the

organization of raw data in table form, usingclasses and frequencies


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GRAPH AND CHART

Graphs and charts help us betterunderstanding the meaning of data. They arecritical for clearly conveying information in

an easy to understand manner as well as in away that the difference between two

different pieces of data is clearly drawn. In away, graphs and charts are illustrative

methods of clearly presenting various typesof differences in a clear method.


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DATA TYPES

1. QUALITATIVE DATA

2. QUANTITATIVE DATA


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QUALITATIVE DATANatural way to organize quantitative data is withthe order property of the real numbers, i.e.,arrange the data from least to greatest.

Example:A sample of 20 M&Ms is observed and theircolors are recorded

Green Yellow Red GreenYellow Brown Red BrownBrown Yellow Blue RedRed Orange Green Yellow

Red Red Yellow Green


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QUALITATIVE DATA

COLOR FREQUENCY PERCENTAGE (%)

Yellow

Green

Red

Brown

Orange

Blue


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LINE GRAPHThe table below shows daily temperatures for Ipoh city, recorded

for 6 days, in degrees Fahrenheit. The data from the table above

has been summarized in the line graph below.


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BAR GRAPHA survey of students' favorite after-school activities was conducted

at a school. The table below shows the results of this survey.

Students' Favorite After-School

Activities

ActivityNumber of

Students

Play Sports 45

Talk on Phone 53

Visit With Friends 99

Earn Money 44

Chat Online 66

School Clubs 22

Watch TV 37


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PIE CHARTA pie graph, also known as a pie chart, is a type of graph commonly used in

conjunction with percentages. A large circle is divided into sections dependingon those percentages and each section represents part of the whole. In a pie

chart, the arc length of each separate sector is meant to be proportional to the

percentage its supposed to represent. A survey of favorite type of movie in a

DIP5


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QUANTITATIVE DATA

Quantitative data is typically organizedby counting instances or events and

displaying the results by class, grade

level, and school. The results can be

displayed in "charts with numbers and

percentages; in simple frequency tables;or in tables showing the mean, median,

and range.


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HISTOGRAM

A graph that uses contiguous vertical barsto display the frequency of the data (unlessthe frequency equals 0) contained in each

class. The heights of the bars equal thefrequency (after certain scale has been

chosen) and the bases of the bars lie on thecorresponding class. It is similar to a BarChart, but a histogram groups numbers

into ranges.
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HISTOGRAM

Example: Draw a histogram for the following data:

Class Interval Frequency

Histogram0 5 4

5

10 10

10 15 18

15 20 8

20 25 6

Histogram


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FREQUENCY POLYGON

Example: Draw a Frequency Polygon to show thenumber of trainers sold in this shop, by age of

customer.

Age of

Customer

Number of Shoes

Sold (f)

Mid Point of Class

(x)

5 - 9

10- 14

15- 19

20 - 24

25 - 29

2

4

5

5

3

7

12

17

22

27


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FREQUENCY POLYGONAge of Customer Number of Shoes Sold

(f)

Mid Point of Class (x)

5 - 9

10 - 14

15 - 19

20 - 24

25 - 29

2

4

5

5

3

7

12

17

22

27

Age (years)

Number (sold)


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OGIVE

Marks 10 - 20 20 - 30 30 - 40 40 - 50 50 - 60 60 - 70

Number of

students7 10 23 51 6 3

Marks No. of students (f)Cumulative

Frequency (cf)

0 - 10 0 0

10 - 20 7 1720 - 30 10 17

30 - 40 23 40

40 - 50 51 91

50 - 60 6 97

60 - 70 2 100

Example: Draw cumulative frequency curve andcumulative frequency polygon for the frequency distribution

by less than type method.

Solution:


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OGIVEMarks No. of students (f) Cumulative Frequency (cf)

0 - 10 0 0

10 - 20 7 17

20 - 30 10 17

30 - 40 23 40

40 - 50 51 91

50 - 60 6 97

60 - 70 2 100

intro of statistics - ogive

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