g) Data Handling - Student.ppt

8/9/2019 g) Data Handling - Student.ppt

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Data HandlingCollecting Data

Learning Outcomes

Understand terms: sample, population, discrete, continuous andvariable

Understand the need for different sampling techniques including

random and stratified sampling and be able to generate randomnumbers with a calculator or computer to obtain a sample

Be able to design a questionnaire (taking bias into account)

Understand the need for grouping data and the importance ofclass limits and class boundaries when doing so


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DH !ollecting Data Data Handling

"ample: # sample is a subset of the population$ %%# would be a subset of the

following populations & 'ear %%, senior pupils, pupils of "t ar's

*opulation:

+he total number of individuals or obects being anal'-ed. this quantit' isuser defined$ /$g$ pupils in a school, people in a town, people in a postal

code$

Discrete:

# discrete variable is often associated with a count, the' can onl' take

certain values 0 usuall' whole numbers$

/$g$ number of children in a famil', number of cars in a street, number of

people in a class$


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!ontinuous:

# continuous variable is often associated with a measurement, the' can

take an' value in given range$

/$g$ height, weight, time$

1ariable:"ee discrete 2 continuous above$


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3andom "ampling:4n simple random sampling ever' member of the population is a given

number$ 4f the population has %55 member , the' will each be given a

number between 555 and 666 (inclusive) then 7 digit random numbers are

used to select the sample (ignore repeats)

"tratified "ample:

8ften data is collected in sections (strata)$

/g$ 9umber of pupils in a school$ 4n selecting

such a sample data is taken as a proportion ofthe total population$ Here we should sample

twice as man' people in 'ear %5 than in

'ear $

;ear 9o$ of *upils

%55

6


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"tratified "ample:

+o obtain as sample of >5 pupils out of the >55, we construct the

following table

;ear 9o$ of*upils

*roportion of total 9o$ of pupils to be sampled

%55 %55?>55 @%?>

%55?>55 @%?> A >5 @ %5

6 55 @%?% A >5 @ <

%5 =55 =55?>55 @ =?> %55?>55 @ =?> A >5 @ =5

%% =55 =55?>55 @=?>

%55?>55 @=?> A >5 @ =5

%= %55 @7?% A >5 @ %<

>55 >5


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DH !ollecting Data Questionnaires

%$ "ample should represent population

=$ "ample must be of a reasonable si-e to represent population

(at least 75) sample mean @ population mean

7$ Cuestions should:

i) be as short as possible

ii) use tick boes

iii) avoid bias

iv) avoid leading questions


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Additional Notes


8/27

Data HandlingCollecting Data

Understand terms: sample, population, discrete,

continuous and variable

Understand the need for different sampling techniques

including random and stratified sampling and be able to

generate random numbers with a calculator or computer

to obtain a sample

Be able to design a questionnaire (taking bias into

account)

Understand the need for grouping data and the

importance of class limits and class boundaries

Learning Outcomes:

At the end of the topic I will be able to

Can Reise

Do !urther


9/27

Data HandlingAnal"sing Data

Learning Outcomes

Understand that in order to gain a mental picture of a collectionof data it is necessar' to obtain a measure of average and range

Be able to determine the mean, median and mode for a set of

raw scores and an ungrouped frequenc' table

Be able to obtain the median and interquartile range for groupeddata from a cumulative frequenc' graph

Understand the advantages and disadvantages of each averageand measure of spread


10/27

DH #nal'sing Data#easures of

Central $endenc"

ean"um of all measures divided b' total number of measures$

n x

x ∑=

ode

ost popular ? most frequent occurrence$

ever'one included

A affected b' etremes

A not ever'one included not affected b' etremes

edian

#rrange data in ascending order. the median is the middle

measure$ *osition @ E (n F %)

A not ever'one included not affected b' etremes


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DH #nal'sing Data#easures of

Central $endenc"

/amples!alculate the ean, edian and ode for:

a) 7, ,


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DH #nal'sing Data !re%uenc" Distribution

+he number of children in 75 families surve'ed are surve'ed$

+he results are given below$

!alculate

a) +he mean number

of children per famil'

b) +he median

(9o$ of children)

x 5 % = 7 <

(9o of families)

f

< %5 G 7 =


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DH #nal'sing Data&rouped !re%uenc"

Distribution

8ften data is grouped so that patterns and the shape of the distribution can be

seen$ Iroup si-es can be the same, although there are no applicable rules$

Jind the mean of:

ark Jrequenc' ( f ) idpoint ( x) fx

75 0 7 >

5 0 6 %


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DH #nal'sing DataCumulatie

!re%uenc" Cures

Jind the median of the following grouped frequenc' distribution$

Kength Jrequenc'!umulativeJrequenc'

Upper Kimit

=% 0 = 7

=< 0 = >

=6 0 7= %=77 0 7G G

7> 0 5


15/27

DH #nal'sing DataCumulatie

!re%uenc" Cures

! u m u l a t i v e f r e q u e n c '

Upper Kimit

C7

C=

C%

edian @ easure of central location

4nterquartile range @ easure of spread C% @ =


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DH #nal'sing Data Additional Notes

D t H dli


17/27

Data HandlingAnal"sing Data

Learning Outcomes:

At the end of the topic I will be able to

Can Reise

Do !urther

Understand that in order to gain a mental picture of acollection of data it is necessar' to obtain a measureof average and range

Be able to determine the mean, median and mode

for a set of raw scores and an ungrouped frequenc'table

Be able to obtain the median and interquartile rangefor grouped data from a cumulative frequenc' graph

Understand the advantages and disadvantages of


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D t H dli


19/27

Data Handling'resenting Data

Learning Outcomes

3evise drawing of pie charts, line graphs and bar charts

Be able to present data using a stem and leaf diagram, determine

mean, edian and quartiles

Be able to draw a boplot for a set of values and compare more thanone bo and whisker plots with reference to their average, spread,

skewness

Be able to draw a histogram to represent groups with unequal widths

Nnow which diagram to use to represent data, the advantages anddisadvantages of each t'pe$


20/27

DH *resenting Data (o) * +his,er 'lots

# bo 2 Ohisker plot illustrates:a) +he range of data

b) +he median of data

c) +he quartiles and interquartile range of data

d) #n' indication of skew within the data

"cale

Q- Q. Q/


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DH *resenting Data 0catter Diagrams

y

x

×

×

×

××

×

× ×

×

y

x

××

×

×

×

×

×

× ×

*ositive !orrelation

x P yP

9egative !orrelation

x ▲ y▼

+he closer the points, the stronger the correlation

y

x

×

×

×

×

×

×

×

×

×

9o !orrelation

x 2 y are independent

× ×

×

×


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DH *resenting Data Histograms

7= packages were brought to the local post office$ +he masses of the packages

were recorded as follows

#ass 1g2 5 Q m R 75 75 Q m R 5 5 Q m R


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DH *resenting Data Histograms

&roup !re%uenc" Class +idth!re%uenc"

Densit"

5 Q m R 75 7 75

75 Q m R 5 %5 %5

5 Q m R


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DH *resenting Data 0tem * Leaf Diagram

Ohen data are grouped to draw a histogram or a cumulative frequenc'distribution, individual results are lost$ +he advantage of grouping is that

patterns (distribution) can be seen$ 4n a stem and leaf diagram individual

results are retained and the spread ? distribution of the data can be seen$

Draw a stem and leaf diagram for the data:

%5, %%, %=, %


25/27

DH *resenting Data Additional Notes


26/27

Data Handling


27/27

Data Handling'resenting Data

Can Reise

Do !urther

3evise drawing of pie charts, line graphs and bar charts

Be able to present data using a stem and leaf diagram,determine mean, edian and quartiles

Be able to draw a boplot for a set of values andcompare more than one bo and whisker plots with

reference to their average, spread, skewness

Be able to draw a histogram to represent groups withunequal widths

Nnow which diagram to use to represent data, theadvantages and disadvantages of each t'pe$

g) Data Handling - Student.ppt

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