7/25/2019 Meaning of Statistics.docx

http://slidepdf.com/reader/full/meaning-of-statisticsdocx 1/8

Assignment

in Statistics

Submittedby:

Czarina

Isabela P.Tuazon

7/25/2019 Meaning of Statistics.docx

http://slidepdf.com/reader/full/meaning-of-statisticsdocx 2/8

Meaning of StatisticsStatistics is the study of the collection, analysis, interpretation, presentation, and organization of data. In applying

statistics to, e.g., a scientific, industrial, or social problem, it is conventional to begin with a statistical population o

a statistical model process to be studied. Populations can be diverse topics such as "all people living in a country"

or "every atom composing a crystal". Statistics deals with all aspects of data including the planning of data

collection in terms of the design of  surveys andexperiments.

Some popular definitions are:

Merriam-Webster dictionary defines statistics as "classified

facts representing the conditions of a people in a state especially the facts that can be stated in numbers

or any other tabular or classified arrangement

7/25/2019 Meaning of Statistics.docx

http://slidepdf.com/reader/full/meaning-of-statisticsdocx 3/8

Statistician Sir Arthur Lyon Bowley defines statistics as

"!umerical statements of facts in any department of inuiry placed in relation to each other 

https:##en.wi$ipedia.org#wi$i#Statist

Populations andSamples

%he study of statistics revolves around the study of data sets. %his lesson describes two important types of datasets & populations and samples. 'long the way, we introduce simple random sampling, the main method used in

this tutorial to select samples.

Population vs Sample

%he main difference between a population and sample has to do with how observations are assigned to the data

set.

 ' population includes all of the elements from a set of data.

7/25/2019 Meaning of Statistics.docx

http://slidepdf.com/reader/full/meaning-of-statisticsdocx 4/8

 ' sample consists of one or more observations from the population.

(epending on the sampling method, a sample can have fewer observations than the population, the same numbe

of observations, or more observations. )ore than one sample can be derived from the same population.

*ther differences have to do with nomenclature, notation, and computations. +or example,

 ' a measurable characteristic of a population, such as a mean or standard deviation, is called aparamete

but a measurable characteristic of a sample is called a statistic.

-e will see in future lessons that the mean of a population is denoted by the symbol but the mean of a

sample is denoted by the symbol x.

-e will also learn in future lessons that the formula for the standard deviation of a population is different

from the formula for the standard deviation of a sample.

-hat is Simple /andom Sampling0

' sampling method is a procedure for selecting sample elements from a population. Simple random

sampling refers to a sampling method that has the following properties.

%he population consists of N  ob1ects.

%he sample consists of n ob1ects.

 'll possible samples of n ob1ects are eually li$ely to occur.

'n important benefit of simple random sampling is that it allows researchers to use statistical methods to analyzesample results. +or example, given a simple random sample, researchers can use statistical methods to define

a confidence interval around a sample mean. Statistical analysis is not appropriate when non&random sampling

methods are used.

%here are many ways to obtain a simple random sample. *ne way would be the lottery method. 2ach of

the N  population members is assigned a uniue number. %he numbers are placed in a bowl and thoroughly mixed

%hen, a blind&folded researcher selects n numbers. Population members having the selected numbers are include

in the sample.

http:##stattre$.com#sampling#populations&and&samples.as

7/25/2019 Meaning of Statistics.docx

http://slidepdf.com/reader/full/meaning-of-statisticsdocx 5/8

Variable and Data' variable  is any characteristics, number, or uantity that can be measured or counted. ' variable may also

called a data item. 'ge, sex, business income and expenses, country of birth, capital expenditure, class grade

eye colour and vehicle type are examples of variables.

What Are Variables?

In statistics, a variable has two defining characteristics:

 ' variable is an attribute that describes a person, place, thing, or idea.

%he value of the variable can "vary" from one entity to another.

+or example, a person3s hair color  is a potential variable, which could have the value of "blond" for one person an

"brunette" for another.

ualitative vs! uantitative Variables

4ariables can be classified as "ualitative 5a$a, categorical6 or "uantitative 5a$a, numeric6.

7ualitative. 7ualitative variables ta$e on values that are names or labels. %he color of a ball 5e.g., red,

green, blue6 or the breed of a dog 5e.g., collie, shepherd, terrier6 would be examples of ualitative or

categorical variables.

7uantitative. 7uantitative variables are numeric. %hey represent a measurable uantity. +or example, whe

we spea$ of the population of a city, we are tal$ing about the number of people in the city & a measurable

attribute of the city. %herefore, population would be a uantitative variable.

In algebraic euations, uantitative variables are represented by symbols 5e.g., x , y , or z 6.

7/25/2019 Meaning of Statistics.docx

http://slidepdf.com/reader/full/meaning-of-statisticsdocx 6/8

#iscrete vs! $ontinuous Variables

7uantitative variables can be further classified as discrete or continuous. If a variable can ta$e on any value

between its minimum value and its maximum value, it is called a continuous variable otherwise, it is called a

discrete variable.

Some examples will clarify the difference between discrete and continouous variables.

Suppose the fire department mandates that all fire fighters must weigh between 89 and ;9 pounds. %he

weight of a fire fighter would be an example of a continuous variable since a fire fighter3s weight could ta$

on any value between 89 and ;9 pounds.

Suppose we flip a coin and count the number of heads. %he number of heads could be any integer value

between and plus infinity. <owever, it could not be any number between and plus infinity. -e could not

for example, get ;.= heads. %herefore, the number of heads must be a discrete variable.

%nivariate vs! Bivariate #ata

Statistical data are often classified according to the number of variables being studied.

%nivariate data. -hen we conduct a study that loo$s at only one variable, we say that we are wor$ing wit

univariate data. Suppose, for example, that we conducted a survey to estimate the average weight of high

school students. Since we are only wor$ing with one variable 5weight6, we would be wor$ing with univariate

data.

Bivariate data. -hen we conduct a study that examines the relationship between two variables, we are

wor$ing with bivariate data. Suppose we conducted a study to see if there were a relationship between the

height and weight of high school students. Since we are wor$ing with two variables 5height and weight6, we

would be wor$ing with bivariate data.

http:##stattre$.com#descriptive&statistics#variables.as

7/25/2019 Meaning of Statistics.docx

http://slidepdf.com/reader/full/meaning-of-statisticsdocx 7/8

Scales of Measurementin Statistics

)easurement scales are used to categorize and#or uantify variables. %his lesson describes the four scales of

measurement that are commonly used in statistical analysis: nominal, ordinal, interval, and ratio scales.

Properties o& Measurement Scales

2ach scale of measurement satisfies one or more of the following properties of measurement.

'dentity. 2ach value on the measurement scale has a uniue meaning.

Magnitude. 4alues on the measurement scale have an ordered relationship to one another. %hat is, some

values are larger and some are smaller.

("ual intervals. Scale units along the scale are eual to one another. %his means, for example, that the

difference between 8 and ; would be eual to the difference between 8> and ;.

A minimum value o& )ero. %he scale has a true zero point, below which no values exist.

*ominal Scale o& Measurement

%he nominal scale of measurement only satisfies the identity property of measurement. 4alues assigned to

variables represent a descriptive category, but have no inherent numerical value with respect to magnitude.

?ender is an example of a variable that is measured on a nominal scale. Individuals may be classified as "male" o

"female", but neither value represents more or less "gender" than the other. /eligion and political affiliation are oth

examples of variables that are normally measured on a nominal scale.

+rdinal Scale o& Measurement

7/25/2019 Meaning of Statistics.docx

http://slidepdf.com/reader/full/meaning-of-statisticsdocx 8/8

%he ordinal scale has the property of both identity and magnitude. 2ach value on the ordinal scale has a uniue

meaning, and it has an ordered relationship to every other value on the scale.

'n example of an ordinal scale in action would be the results of a horse race, reported as "win", "place", and

"show". -e $now the ran$ order in which horses finished the race. %he horse that won finished ahead of the horse

that placed, and the horse that placed finished ahead of the horse that showed. <owever, we cannot tell from this

ordinal scale whether it was a close race or whether the winning horse won by a mile.

'nterval Scale o& Measurement

%he interval scale of measurement has the properties of identity, magnitude, and eual intervals.

' perfect example of an interval scale is the +ahrenheit scale to measure temperature. %he scale is made up of

eual temperature units, so that the difference between @ and 9 degrees +ahrenheit is eual to the difference

between 9 and A degrees +ahrenheit.

-ith an interval scale, you $now not only whether different values are bigger or smaller, you also $now how

much bigger or smaller they are. +or example, suppose it is A degrees +ahrenheit on )onday and B degrees o

%uesday. Cou $now not only that it was hotter on %uesday, you also $now that it was 8 degrees hotter.

,atio Scale o& Measurement

%he ratio scale of measurement satisfies all four of the properties of measurement: identity, magnitude, eual

intervals, and a minimum value of zero.

%he weight of an ob1ect would be an example of a ratio scale. 2ach value on the weight scale has a uniue

meaning, weights can be ran$ ordered, units along the weight scale are eual to one another, and the scale has a

minimum value of zero.

-eight scales have a minimum value of zero because ob1ects at rest can be weightless, but they cannot have

negative weight. 

http:##stattre$.com#statistics#measurement&scales.aspx0%utorialD'