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8/6/2019 Statistics Sampling and Methods WBHS
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A focus on Sampling andA focus on Sampling and
Sampling MethodsSampling Methods
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MenuMenuSampling Methods
Measures of Centre
Measures of Spread
Definitions
Assessment Tips
Practice Tasks
For clarification, click on any step you do not understand to see that
element broken down
The example used throughout this presentation is trying to find the
mean height of WBHS pupils
On Your Calculator
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Sampling MethodsSampling Methods
In this presentation youIn this presentation you
will see a number ofwill see a number of
sampling methods, theirsampling methods, theirbenefits and drawbacks.benefits and drawbacks.
Simple Random Sample
Cluster Sampling
Systematic Sampling
Stratified Sampling
Note: For more detailed instructions
on any of the example click on
the step you misunderstand
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Measures of Central TendencyMeasures of Central Tendency
In this presentationIn this presentation
you will learn how toyou will learn how to
calculate a number ofcalculate a number ofmeasures of averagemeasures of average
or centre, as well asor centre, as well as
their benefits andtheir benefits and
drawbacksdrawbacks
Mean
Median
Mode
Note: For more detailed instructions
in any of the examples click
on the step you misunderstand
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Measures ofSpreadMeasures ofSpread
In this presentation youIn this presentation you
will learn how to find awill learn how to find a
number of measures ofnumber of measures of
spread as well as theirspread as well as their
drawbacks and advantages.drawbacks and advantages.
You will also need toYou will also need to
decide which measure ofdecide which measure ofspread and which measurespread and which measure
of centre go together.of centre go together.
Standard Deviation
Interquartile Range
Range
Note: For more detailed instructions
in any of the examples click
on the step you misunderstand
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Simple RandomSampleSimple RandomSample
The simplest unbiasedThe simplest unbiased
sample.sample.
11-- Number the entireNumber the entire
population.population.
22-- Generate randomGenerate random
numbers.numbers.
33-- Proceed until you haveProceed until you haveas many as you needas many as you need
ignoring any repeats.ignoring any repeats.
Example (Heights of WBHS students)Example (Heights of WBHS students)
1.1. Get a copy of the School Roll.Get a copy of the School Roll.
2.2. Number every personNumber every person
3.3. Generate Random numbers from 1Generate Random numbers from 1
to the maximum you need.to the maximum you need.
4.4. Proceed until you have the desiredProceed until you have the desired
sample size ignoring repeats.sample size ignoring repeats.
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Simple RandomSampleSimple RandomSample
AdvantagesAdvantages
CheapCheap
Easy to carry outEasy to carry outUnbiasedUnbiased
DisadvantagesDisadvantages
May not represent strataMay not represent strata
Needs an entire populationNeeds an entire populationlistlist
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Cluster SamplingCluster Sampling
The easiest unbiasedThe easiest unbiased
sample.sample.
1.1. Sort your data intoSort your data into
clusters based on location.clusters based on location.
2.2. Randomly choose theRandomly choose the
cluster.cluster.
3.3. Perform a simple randomPerform a simple randomsample on the chosensample on the chosen
cluster.cluster.
Example (Heights of WBHS students)Example (Heights of WBHS students)
1.1. Get a copy of the School Roll.Get a copy of the School Roll.
2.2. Sort into clustersSort into clusters egeg year levelsyear levels
3.3. Randomly select the cluster.Randomly select the cluster.
4.4. Randomly generate a sample fromRandomly generate a sample from
each cluster.each cluster.
Care with clusters as Juniors areCare with clusters as Juniors aremuch shorter than Seniorsmuch shorter than Seniors
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Cluster SamplingCluster Sampling
AdvantagesAdvantages
Very CheapVery Cheap
Very Easy to carry outVery Easy to carry outUnbiasedUnbiased
DisadvantagesDisadvantages
Needs an entire populationNeeds an entire population
listlist
Can be biased if clustersCan be biased if clusters
strongly affect thestrongly affect the
statistics.statistics.
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Systematic SamplingSystematic Sampling
A relatively quick way toA relatively quick way to
pick an unbiased samplepick an unbiased sample
1.1. List the entire population.List the entire population.
2.2. Decide on your step sizeDecide on your step size
(Total(Total Sample size = n)Sample size = n)..
3.3. Randomly generate aRandomly generate a
starting point.starting point.4.4. Step every nStep every nthth data pointdata point
till you have your sample.till you have your sample.
Example (Heights of WBHS students)Example (Heights of WBHS students)
1.1. Get an alphabetical copy of theGet an alphabetical copy of the
School Roll.School Roll.
2.2. StepSize = TotalStepSize = Total Sample sizeSample size
3.3. Randomly generate a starting point.Randomly generate a starting point.
4.4. Starting from the beginning use theStarting from the beginning use the
step size to pick the rest of thestep size to pick the rest of the
samplesample
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Systematic SamplingSystematic Sampling
AdvantagesAdvantages
CheapCheap
Easy to Choose SampleEasy to Choose SampleUnbiasedUnbiased
DisadvantagesDisadvantages
Needs an entire populationNeeds an entire population
listlist
If population list is orderedIf population list is ordered
then sample can becomethen sample can become
biasedbiased
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Stratified SamplingStratified Sampling
The most reliableThe most reliablesampling method.sampling method.
1.1. Sort the data into strataSort the data into strata
based on information youbased on information youalready know.already know.
2.2. Calculate the proportionsCalculate the proportionsfor each strata.for each strata.
3.3. Perform a Simple RandomPerform a Simple RandomSample on each of theSample on each of thestrata.strata.
Example (Heights of WBHS students)Example (Heights of WBHS students)
1.1. Get a copy of the School RollGet a copy of the School Roll
separated into year levels.separated into year levels.
2.2. Calculate the sample size for eachCalculate the sample size for each
year group (strata).year group (strata).
3.3. Performa simple random samplePerforma simple random sample
on each year group to their specificon each year group to their specific
sample size.sample size.
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Stratified SamplingStratified Sampling
AdvantagesAdvantages
UnbiasedUnbiased
CompletelyCompletelyrepresentative of eachrepresentative of each
of the strataof the strata
Most reliable estimatesMost reliable estimates
DisadvantagesDisadvantages
Needs entire populationNeeds entire population
listlist
Information about entireInformation about entire
population needs to bepopulation needs to be
known beforehandknown beforehand
Time consumingTime consuming
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Generate a Random NumberGenerate a Random Number
1.1. Decide on the startingDecide on the starting
number (in this case 1)number (in this case 1)
2.2. Decide how many youDecide how many you
need (In the case of theneed (In the case of the
school 529 students)school 529 students)
3.3. Choose your calculatorChoose your calculator
Casio
FX-82
Casio
Graphic
Texas
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Random Number on a CasioRandom Number on a Casio
Graphics CalculatorGraphics Calculator1.1. Decide on the startingDecide on the starting
number (in this case 1)number (in this case 1)
2.2. Decide how many youDecide how many you
need (In the case of theneed (In the case of the
school 529 students)school 529 students)
3.3. InIn RunRun ModeModeIntgIntg OPTNOPTN F6F6 F4F4 F5F5
Ran#Ran# OPTNOPTN F6F6 F3F3 F4F4
On ScreenOn Screen
IntgIntg(529(529 Ran# + 1)Ran# + 1)
Population sizeor Strata size Starting Value
OPTN
F3 F4 F6
( )
7 8
5
+1
Intg(529 Ran# + 1)
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Random Number on a Casio FXRandom Number on a Casio FX -- 8282
1.1. Decide on the startingDecide on the starting
number (in this case 1)number (in this case 1)
2.2. Decide how many youDecide how many you
need (In the case of theneed (In the case of the
school 529 students)school 529 students)
3.3. Ran# = 2Ran# = 2ndnd functionfunction
4.4. On screenOn screen
Ran#Ran# 529 + 1 =529 + 1 =
notenote Ignore any decimal in theIgnore any decimal in the
answeranswer
Population size
or strata size
Starting value
RAN#529+1
shift
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Random Number on a TexasRandom Number on a Texas
1.1. Decide on the startingDecide on the starting
number (in this case 1)number (in this case 1)
2.2. Decide how many youDecide how many you
need (In the case of theneed (In the case of the
school 529 students)school 529 students)
RANDIRANDI PRBPRB RANDIRANDI
,, 22ndnd Function )Function )
3.3. On ScreenOn Screen
RANDI(1 , 529)RANDI(1 , 529)
End ValueStarting Value
2nd
PRB
)
RANDI(1,529)
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Simple RandomSampleSimple RandomSample
The simplest unbiasedThe simplest unbiasedsample.sample.
1.1. Number the entireNumber the entire
population.population.2.2. Generate randomGenerate random
numbers.numbers.
3.3. Proceed until youProceed until you
have as many as youhave as many as youneed ignoring anyneed ignoring anyrepeats.repeats.
Example (Heights of WBHS students)Example (Heights of WBHS students)
1.1. Get a copy of the School Roll.Get a copy of the School Roll.
2.2. Number every person from 1 (toNumber every person from 1 (to
529)529)
3.3. Generate Random numbers from 1Generate Random numbers from 1
to the maximum you need (529).to the maximum you need (529).
4.4. Proceed until you have the desiredProceed until you have the desired
sample size ignoring repeats.sample size ignoring repeats.
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Strata ProportionsStrata Proportions
1.1. Number of peopleNumber of people
in strata divided byin strata divided by
total in population.total in population.
2.2. Multiplied byMultiplied by
number of peoplenumber of people
wanted in totalwanted in total
sample.sample.
Example (Heights of WBHS students)Example (Heights of WBHS students)
1.1. 529 people on School Roll.529 people on School Roll.
2.2. 115 year 10s115 year 10s
3.3. Sample size of 30Sample size of 30
4.4. So year 10 sample sizeSo year 10 sample size
115115 529529 30 = 6.5230 = 6.52
So take 7 year 10 studentsSo take 7 year 10 students
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Systematic StepSizesSystematic StepSizes
1.1. Number of peopleNumber of people
in populationin population
divided by Sampledivided by Sample
SizeSize
Example (Heights of WBHS students)Example (Heights of WBHS students)
1.1. 529 people on School Roll.529 people on School Roll.
2.2. Sample size of 30Sample size of 30
3.3. So Step sizeSo Step size
529529 30 = 17.6333330 = 17.63333
So take every 17So take every 17thth student from thestudent from the
starting positionstarting position
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Systematic SteppingSystematic Stepping
1.1. Starting at theStarting at the
random start pointrandom start point
step out till you getstep out till you get
desired sample size.desired sample size.
Example (Heights of WBHS students)Example (Heights of WBHS students)
1.1. Random starting point 803, stepRandom starting point 803, step
size 29size 29
2.2. 803803rdrd student on alphabeticallist isstudent on alphabeticallist is
where we start.where we start.
3.3. Then 832Then 832ndnd student, 861student, 861stst student,student,
we have now reached the end of thewe have now reached the end of the
roll so start at the beginning 890=roll so start at the beginning 890=1515thth student then 45student then 45thth studentstudent
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MeanMean1.1. Add up all of theAdd up all of the
values in the sample.values in the sample.
2.2. Divide by the sampleDivide by the sample
size.size.
Advantages
Easy to calculate for large
samples.
Accurate and well understood
Disadvantages
Affected by outliers
Calculator Method
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MedianMedian
1.1. List all the values inList all the values in
order.order.
2.2. Find the central valueFind the central value
Advantages
Accurate
Not affected much by Outliers
Disadvantages
Not so widely known as an
average
Time consuming to list large
sample in order
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ModeMode
1.1. List all the valuesList all the values
2.2. Find the most commonFind the most common
itemitem
Advantages
Can calculate mode for data that
is not numeric or ordered
Not affected much by Outliers
Very easy to calculate
Disadvantages
Can be inaccurate for numeric or
data that can be ordered
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Statistics on a CalculatorStatistics on a Calculator
Choose your calculatorChoose your calculator
Casio
FX-82
Casio
Graphic
Texas
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1.1. In Stat ModeIn Stat Mode
2.2. InIn list 1list 1 enter all data valuesenter all data values
3.3. InIn list 2list 2 enter theirenter their
frequenciesfrequencies
4.4. F2 (CALC)F2 (CALC)
5.5. F6 (SET)F6 (SET) Should readShould read
6.6. ExitExit
7.7. F1 (1VAR)F1 (1VAR)(All Statistics are listed(All Statistics are listed is meanis mean,, n is std. devn is std. dev.).)
F2F1 F6
1Var XList :List1
1Var Freq :List2
2Var XList :List3
2Var YList :List4
2Var Freq :List5
EXIT
Statistics on aStatistics on a
Casio Graphics CalculatorCasio Graphics Calculator
S.D. using table
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Entering Data onEntering Data on
Casio Graphics CalculatorCasio Graphics CalculatorEnter each data valuein List 1 followed by
EXE
Enter the frequency of
each data value in List 2
followed by EXE
Note If all of the frequencies are
1 then you dont need to
enter the frequencies.
In the Set Menu change the 1Var Freq
to 1 instead of list 2
List 1 List 2 List 3 List4
1
2
3
4
5
EXE
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1.1. Put your calculator intoPut your calculator into
statistics modestatistics mode Mode 2Mode 2
2.2. Clear the statistics memoryClear the statistics memory Shift Mode 1Shift Mode 1
3.3. Enter the data carefullyEnter the data carefully 180cm M+180cm M+
4.4. Calculate desired statisticsCalculate desired statistics Shift 2Shift 2
1.1. meanmean
2.2. nn standard deviationstandard deviation
Statistics on aStatistics on a
Casio FX 82 CalculatorCasio FX 82 CalculatorScl mode clr all
1 2 3
shift mode
M+
Shown on Screen
S.D. using table
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Entering Data onEntering Data on
Casio FX 82 CalculatorCasio FX 82 Calculator
Enter each data value
followed by M+
n is the number of data
values that you have entered
Note Be very careful entering thedata values as you cannot
review them later to make
sure that they are correct.
n =
1
M+
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Statistics on aStatistics on a
Texas CalculatorTexas Calculator1.1. Put your calculator intoPut your calculator intostatistics modestatistics mode
1.1. 22ndnd Function DATAFunction DATA
2.2. 11 -- VARVAR
2.2. Enter the data carefullyEnter the data carefully
1.1. DATADATA
3.3. Calculate desired statisticsCalculate desired statistics
1.1. STATVARSTATVAR
2.2. Shift between statistics with arrowShift between statistics with arrowkeyskeys
1.1. nn number of data valuesnumber of data values
2.2. meanmean
3.3. standard deviationstandard deviation
S.D. using table
2nd
DATA
n x Sx x
STATVAR
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Entering Data on aEntering Data on a
Texas CalculatorTexas Calculator
2nd
DATA
X1 = 180
Press the Data Key
to begin
Begin entering data.
X1 is the data value
Followed by the down arrow
Freq1 is that data values frequencyFollowed by the down arrow
X2 is next then Freq2
To check data use up arrow
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DefinitionsDefinitions
PopulationPopulation The entire list of those people or things that you wishThe entire list of those people or things that you wishto sampleto sample
CensusCensus A survey of anA survey of an entire populationentire population
SampleSample A small group of a populationA small group of a population
ParametersParameters Facts about an entire populationFacts about an entire population gained from a censusgained from a census
(Notation: mean (Notation: mean or standard deviation or standard deviation ))
StatisticsStatistics Estimates of population parametersEstimates of population parameters calculated from acalculated from asamplesample
(Notation: mean (Notation: mean or standard deviation s) or standard deviation s)
RepresentativeRepresentative A sample that appears toA sample that appears to represent all elements of therepresent all elements of the
in the correct proportionsin the correct proportionspopulationpopulation BiasBias A sampling method thatA sampling method that does not give every element ofdoes not give every element of
the population an equal chance of selectionthe population an equal chance of selection
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Standard DeviationStandard Deviation This is a calculation of theThis is a calculation of the
average difference betweenaverage difference betweenthe data values and thethe data values and themean.mean.
This measure of spreadThis measure of spreadapplies to the mean.applies to the mean.
Advantages
Easy to calculate for large
samples on calculator.
Accurate
Very useful for certain types of
data
Disadvantages
Affected by outliers
Possibly not so well understood
Use Calculatorto Calculate Use table to calculate
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Interquartile RangeInterquartile Range1.1. Calculate the upper andCalculate the upper and
lower quartiles.lower quartiles.
2.2. Upper quartile minus lowerUpper quartile minus lowerquartile.quartile.
3.3. This measure of spreadThis measure of spreadapplies to the medianapplies to the median
Advantages
Well understood
Unaffected by outliers
Disadvantages
Easy to calculate for large
samples.
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1.1. Find the highest and lowestFind the highest and lowestvalue.value.
2.2. Highest value minus theHighest value minus thelowest value.lowest value.
3.3. This measure of spreadThis measure of spreadapplies to all measures ofapplies to all measures ofcentre.centre.
RangeRange
Advantages
Well understood
Unaffected by outliers
Disadvantages
Easy to calculate for large
samples.
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Standard Deviation by TableStandard Deviation by Table
( )2
180 165 15 225
150 165 -15 225
165 165 0 0
170 165 5 25
160 165 -5 25
Total 825 0 500
Mean 165 100
Data Values
From your sample
or census
Mean
Calculated as usual,
doesnt change Data values minus the Mean
Square of each ofthe values to the left
Final Standard Deviation
is the square root of this
value so s = 10
Use Calculator to Calculate
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1.1. List all the values in order.List all the values in order.
2.2. Find the central valueFind the central value
3.3. Discard that central valueDiscard that central value
4.4. Find the central value of theFind the central value of the
remaining two halves.remaining two halves.
5.5. These 2 numbers are theThese 2 numbers are the
upper and lower quartilesupper and lower quartiles
Calculating QuartilesCalculating Quartiles
Example (Heights of WBHS students)Example (Heights of WBHS students)
1.1. Data ValuesData Values
165, 170, 173, 180, 182, 183, 191, 192165, 170, 173, 180, 182, 183, 191, 192
2.2. Central value middle of 180 and 182Central value middle of 180 and 182
so median is 181so median is 181
3.3. Discard 181 and calculate middle ofDiscard 181 and calculate middle of
each half.each half.
4.4. 165, 170, 173, 180//182, 183, 191, 192165, 170, 173, 180//182, 183, 191, 192
Lower quartile Upper quartileLower quartile Upper quartile
171171 187187
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Things to ConsiderThings to Consider
Is my sample representative of the population?
Need to consider whether any strata present in the data are
represented in approximately the correct proportions.
Need to consider the presence of any apparent outliers in the sample
chosen, and the effect they will have on estimates of population
parameters.
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Things to ConsiderThings to Consider
Is my sample representative of the population?
Estimates are more reliable when taken from a large sample as the
effects of outliers are lessened.
Consider the size of the s.d.
A larger value of s suggests considerable variation in the data
values. Thus taking another sample could produce quite different
statistics.
Ask yourself, IfI were to repeat this sampling process, would I getthe same results?
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Things to ConsiderThings to Consider
How could I improve my sampling method?
Need to choose a sampling method which eliminates bias, and which
gives the best chance of choosing a representative sample. (Bias
exists when some of the population members have greater or lesser
chance of being included in the sample.)
Need to discuss which statistics would give the best estimates of
population parameters, including the effect of outliers.
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Things to ConsiderThings to Consider
Would I get the same or similar results if I repeated
the same process?
Are there outliers or extreme values that may affect the samplestatistics? If so then I probably wouldnt get similar results.
Is the standard deviation (or measure of spread) large when
compared to the mean, if it is then repeating the same results is
unlikely.
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Things to ConsiderThings to Consider
When answering question or stating conclusions;
Answers need to be precise and refer to actual data values present in
the sample and/or population.
Strata must be clearly defined.
Answers cannot be vague or rote-learnt without referring specifically
to the context of the assessment.
Students must be very clear that the sample statistics are ESTIMATES
of the population parameters.
They must NOT state that the population mean is unless they have
taken a census of the whole population!
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Practice TasksPractice Tasks
Real Estate Stats
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On Your CalculatorOn Your Calculator
In this part of theIn this part of the
presentation you canpresentation you can
check on exactly howcheck on exactly how
to use your calculatorto use your calculator
effectively to help witheffectively to help with
StatisticsStatistics
Generating Random Numbers
Entering Data
Calculating Statistics
Note: For more detailed instructions
on any of the example click on
the step you misunderstand
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Entering Data on a CalculatorEntering Data on a Calculator
Choose your calculatorChoose your calculator
Casio
FX-82
Casio
Graphic
Texas
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Statistics on a CalculatorStatistics on a Calculator
Choose your calculatorChoose your calculator
Casio
FX-82
Casio
Graphic
Texas
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1.1. In Stat ModeIn Stat Mode
2.2. InIn list 1list 1 enter all data valuesenter all data values
3.3. InIn list 2list 2 enter theirenter their
frequenciesfrequencies
4.4. F2 (CALC)F2 (CALC)
5.5. F6 (SET)F6 (SET) Should readShould read
6.6. ExitExit7.7. F1 (1VAR)F1 (1VAR)(All Statistics are listed(All Statistics are listed is meanis mean,, n is std. devn is std. dev.).)
F2F1 F6
1Var XList :List1
1Var Freq :List2
2Var XList :List3
2Var YList :List4
2Var Freq :List5
EXIT
Statistics on aStatistics on a
Casio Graphics CalculatorCasio Graphics Calculator
S.D. using table
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Entering Data onEntering Data on
Casio Graphics CalculatorCasio Graphics CalculatorEnter each data valuein List 1 followed by
EXE
Enter the frequency of
each data value in List 2
followed by EXE
Note If all of the frequencies are
1 then you dont need to
enter the frequencies.
In the Set Menu change the 1Var Freq
to 1 instead of list 2
List 1 List 2 List 3 List4
1
2
3
4
5
EXE
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1.1. Put your calculator intoPut your calculator into
statistics modestatistics mode Mode 2Mode 2
2.2. Clear the statistics memoryClear the statistics memory Shift Mode 1Shift Mode 1
3.3. Enter the data carefullyEnter the data carefully 180cm M+180cm M+
4.4. Calculate desired statisticsCalculate desired statistics Shift 2Shift 2
1.1. meanmean
2.2. nn standard deviationstandard deviation
Statistics on aStatistics on a
Casio FX 82 CalculatorCasio FX 82 CalculatorScl mode clr all
1 2 3
shift mode
M+
Shown on Screen
S.D. using table
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Entering Data onEntering Data on
Casio FX 82 CalculatorCasio FX 82 Calculator
Enter each data value
followed by M+
n is the number of data
values that you have entered
Note Be very careful entering thedata values as you cannot
review them later to make
sure that they are correct.
n =
1
M+
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Statistics on aStatistics on a
Texas CalculatorTexas Calculator1.1. Put your calculator intoPut your calculator into
statistics modestatistics mode
1.1. 22ndnd Function DATAFunction DATA
2.2. 11 -- VARVAR
2.2. Enter the data carefullyEnter the data carefully
1.1. DATADATA
3.3. Calculate desired statisticsCalculate desired statistics
1.1. STATVARSTATVAR
2.2. Shift between statistics with arrowShift between statistics with arrowkeyskeys
1.1. nn number of data valuesnumber of data values
2.2. meanmean
3.3. standard deviationstandard deviation
S.D. using table
2nd
DATA
n x Sx x
STATVAR
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Entering Data on aEntering Data on a
Texas CalculatorTexas Calculator
2nd
DATA
X1 = 180
Press the Data Key
to begin
Begin entering data.
X1 is the data value
Followed by the down arrow
Freq1 is that data values frequencyFollowed by the down arrow
X2 is next then Freq2
To check data use up arrow
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Generate a Random NumberGenerate a Random Number
1.1. Decide on the startingDecide on the starting
number (in this case 1)number (in this case 1)
2.2. Decide how many youDecide how many you
need (In the case of theneed (In the case of theschool 529 students)school 529 students)
3.3. Choose your calculatorChoose your calculator
Casio
FX-82
Casio
Graphic
Texas
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Random Number on a CasioRandom Number on a Casio
Graphics CalculatorGraphics Calculator
1.1. Decide on the startingDecide on the starting
number (in this case 1)number (in this case 1)
2.2. Decide how many youDecide how many you
need (In the case of theneed (In the case of theschool 529 students)school 529 students)
3.3. InIn RunRun ModeModeIntgIntg OPTNOPTN F6F6 F4F4 F5F5
Ran#Ran# OPTNOPTN F6F6 F3F3 F4F4
On ScreenOn Screen
IntgIntg(529(529 Ran# + 1)Ran# + 1)
Population size
or Strata size Starting Value
OPTN
F3 F4 F6
( )
7 8
5
+1
Intg(529 Ran# + 1)
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Random Number on a Casio FXRandom Number on a Casio FX -- 8282
1.1. Decide on the startingDecide on the starting
number (in this case 1)number (in this case 1)
2.2. Decide how many youDecide how many you
need (In the case of theneed (In the case of the
school 529 students)school 529 students)
3.3. Ran# = 2Ran# = 2ndnd functionfunction
4.4. On screenOn screen
Ran#Ran# 529 + 1 =529 + 1 =
notenote Ignore any decimal in theIgnore any decimal in the
answeranswer
Population size
or strata size
Starting value
RAN#529+1
shift
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Random Number on a TexasRandom Number on a Texas
1.1. Decide on the startingDecide on the starting
number (in this case 1)number (in this case 1)
2.2. Decide how many youDecide how many you
need (In the case of theneed (In the case of theschool 529 students)school 529 students)
RANDIRANDI PRBPRB RANDIRANDI
,, 22ndnd Function )Function )3.3. On ScreenOn Screen
RANDI(1 , 529)RANDI(1 , 529)
E d V lSt ti V l
2nd
PRB
)
RANDI(1,529)