20140211 02 descriptive statisctics

8/11/2019 20140211 02 Descriptive Statisctics

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Statistika RekayasaTabular & Graphical

Types of data

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Categorical data (qualitative data)

Categorical DataUse labels or names to identify an attribute of each

element.Use either the nominal scale or ordinal scale ofmeasurement and may be nonnumeric or numeric.

The statistical analysis for qualitative data are ratherlimited

Categorical variable is a variable with categoricaldataExamle!

Car tye "sedan# sort car# $U%# minivan# &'%# and soon(

&ethod of ayment "cash# credit card# chec)(

*

Data set for 2 !utual fu"ds

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#ua"titative data

,uantitative data

,uantitative data are always numeric.

Use either the interval or ratio scale of measurement.-rdinary arithmetic oerations are meaningful onlywith quantitative data.

,uantitative variable is a variable withquantitative data.

Discrete if they are countable data and are collectedby counting. Ex! the number of items

Continuous if they are collected by measuring andare exressed on a continuous scale. Ex! time tofailure of um comonent

#uestio"$ %hats the type of these data'

Tyes of shis

Categorical

/T$' students collecting data on the numberof shis entering inner channel of $urabaya

0est 1ccess Channel in a articular day.

#ua"titative discrete

Time until a fuel oil simlex filter getting

clogged u.

#ua"titative co"ti"uous


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Tabular a"d graphical !ethods for

su!!arii"g data

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Su!!arii"g categoricalqualitative data

4requency Distribution

5elative 4requency

'ercent 4requency Distribution6ar 7rah

'ie Chart

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*reque"cy distributio"

+ freque"cy distributio" is a tabular

summary of data showing the frequency "or

number( of items in each of several

nonoverlaing classes.

The ob9ective is to provide i"sights about the

data that cannot be quic)ly obtained by

loo)ing only at the original data.

:

,-a!ple$ .arada /""

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,-a!ple$ .arada /""

;;

Relative freque"cy distributio"

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0erce"t freque"cy distributio"

The perce"t freque"cy of a class is the

relative frequency multilied by ;


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1ar graph

1 bar graph is a grahical device for deictingqualitative data that have been summari=ed in a

frequency# relative frequency# or ercentfrequency distribution.

-n the hori=ontal axis we secify the labels thatare used for each of the classes.

1 freque"cy# relative freque"cy# or perce"tfreque"cy scale can be used for the vertical axis.

Using a bar of fixed width drawn above each

class label# we extend the height aroriately.The bars are separated to emhasi=e the factthat each class is a searate category.

;

1ar graph .arada /""

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0ie chart

The pie chart is a commonly used grahicaldevice for resenting relative frequency

distributions for qualitative data.4irst draw a circle> then use the relativefrequencies to subdivide the circle intosectors that corresond to the relativefrequency for each class.

$ince there are *< degrees in a circle# a class

with a relative frequency of


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,-a!ple .arada /""

@nsights 7ained from the'receding 'ie Chart

-nehalf of the customers surveyedgave &arada a quality rating of Aabove averageB or AexcellentB"loo)ing at the left side of the ie(.This might lease the manager.

4or each customer who gave anAexcellentB rating# there were t%o

customers who gave a AoorB rating"loo)ing at the to of the ie(. Thisshould dislease the manager.

;:

,-a!ple *ive popular softdri"ks

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Su!!arie of qua"titative data

4requency Distribution

5elative 4requency and 'ercent 4requency

Distributions

Dot 'lot

istogram

Cumulative Distributions

-give

2*

,-a!ple$ 4udso" +uto Repair

2+

The manager of udson 1uto would li)e to get a bettericture of the distribution of costs for engine tuneu arts. 1samle of < customer invoices has been ta)en and the costs

of arts# rounded to the nearest dollar# are listed below.


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7uidelines for $electing umber of Classes

Use between and 2< classes.

1roximate formula to calculate number of

class may also be introduced as!

ra"ge 5 largest data value s!allest data value

class 5 k 5 67838 log 9: %here 9 is "u!ber of sa!ples

i"terval 5 ra"geclass

Data sets with a larger number of elements usuallyrequire a larger number of classes.

$maller data sets usually require fewer classes.

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7uidelines for selecting width of classes

Use classes of equal width.

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Approximate class width =


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4requency distribution


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2:

@nsights gained from the ercent frequencydistribution!

-nly + of the arts costs are in the F


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*;

4istogra!

1nother common grahical resentation ofquantitative data is a histogram.

The variable of interest is laced on the

hori=ontal axis and the frequency# relativefrequency# or ercent frequency is laced on thevertical axis.

1 rectangle is drawn above each class intervalwith its height corresonding to the intervalGsfrequency# relative frequency# or ercentfrequency.

Unli)e a bar grah# a histogram has no naturalsearation between rectangles of ad9acentclasses.

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**

Cu!ulative distributio"

The cumulative frequency distribution showsthe number of items with values less than orequal to the uer limit of each class.

The cumulative relative frequencydistribution shows the roortion of itemswith values less than or equal to the uerlimit of each class.

The cumulative ercent frequencydistribution shows the ercentage of items

with values less than or equal to the uerlimit of each class.

*+


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*

;give

1n ogive is a graph of a cu!ulative distributio".

The data values are shown on the hori=ontalaxis.

$hown on the vertical axis are the!cumulative frequencies# or

cumulative relative frequencies# or

cumulative ercent frequencies

The frequency "one of the above( of each class islotted as a oint.

The lotted oints are connected by straightlines.

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-give

6ecause the class limits for the artscost data

are


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,-ploratory data a"alysis

The techniques of exloratory data analysis

consist of simle arithmetic and easytodraw

ictures that can be used to summari=e data

quic)ly.

-ne such technique is the stemandleaf

dislay.

*:

Ste!


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+;

Stretched ste!


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+*

Ste!


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,-a!ple$ =eaf u"it 5 >36

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,-a!ple$ =eaf u"it 5 6>

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Crosstabulatio"s a"d scatter diagra!s

Thus far we have focused on methods that

are used to summari=e the data for one

variable at a time.

-ften a manager is interested in tabular and

grahical methods that will hel understand

the relationshi between two variables.

Crosstabulation and a scatter diagram are

two methods for summari=ing the data fortwo "or more( variables simultaneously.

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Crosstabulatio"

Crosstabulation is a tabular method for

summari=ing the data for two variables

simultaneously.

Crosstabulation can be used when!

-ne variable is qualitative and the other is

quantitative

6oth variables are qualitative

6oth variables are quantitative

The left and to margin labels define theclasses for the two variables.

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,-a!ple$ *i"ger =akes 4o!es

+:

Crosstabulation

The number of 4inger Ha)es homes sold for each styleand rice for the ast two years is shown below.

,-a!ple$ *i"ger =akes 4o!es

20140211 02 descriptive statisctics

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