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A focus on Sampling andA focus on Sampling and
Sampling MethodsSampling Methods
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
Sampling MethodsSampling Methods
In this presentation you In this presentation you will see a number of will see a number of sampling methods, their sampling methods, their benefits 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
Measures of Central TendencyMeasures of Central Tendency
In this presentation In this presentation you will learn how to you will learn how to calculate a number of calculate a number of measures of average measures of average or centre, as well as or centre, as well as their benefits and their benefits and drawbacksdrawbacks
Mean
Median
Mode
Note: For more detailed instructions in any of the examples click
on the step you misunderstand
Measures of SpreadMeasures of Spread
In this presentation you In this presentation you will learn how to find a will learn how to find a number of measures of number of measures of spread as well as their spread as well as their drawbacks and advantages.drawbacks and advantages.
You will also need to You will also need to decide which measure of decide which measure of spread and which measure spread 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
Simple Random SampleSimple Random Sample
The simplest unbiased The simplest unbiased sample. sample.
1-1- Number the entire Number the entire population.population.
2-2- Generate random Generate random numbers.numbers.
3-3- Proceed until you have Proceed until you have as many as you need as 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 1 Generate Random numbers from 1 to the maximum you need.to the maximum you need.
4.4. Proceed until you have the desired Proceed until you have the desired sample size ignoring repeats.sample size ignoring repeats.
Simple Random SampleSimple Random Sample
AdvantagesAdvantages
Cheap Cheap
Easy to carry outEasy to carry out
UnbiasedUnbiased
DisadvantagesDisadvantages
May not represent strataMay not represent strata
Needs an entire population Needs an entire population listlist
Cluster SamplingCluster Sampling
The easiest unbiased The easiest unbiased sample. sample.
1.1. Sort your data into Sort your data into clusters based on location.clusters based on location.
2.2. Randomly choose the Randomly choose the cluster.cluster.
3.3. Perform a simple random Perform a simple random sample on the chosen sample 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 clusters eg year levelsSort into clusters eg year levels
3.3. Randomly select the cluster.Randomly select the cluster.
4.4. Randomly generate a sample from Randomly generate a sample from each cluster.each cluster.
Care with clusters as Juniors are Care with clusters as Juniors are much shorter than Seniorsmuch shorter than Seniors
Cluster SamplingCluster Sampling
AdvantagesAdvantages
Very Cheap Very Cheap
Very Easy to carry outVery Easy to carry out
UnbiasedUnbiased
DisadvantagesDisadvantages
Needs an entire population Needs an entire population listlist
Can be biased if clusters Can be biased if clusters strongly affect the strongly affect the
statistics. statistics.
Systematic SamplingSystematic Sampling
A relatively quick way to A relatively quick way to pick an unbiased sample pick an unbiased sample
1.1. List the entire population.List the entire population.
2.2. Decide on your step size Decide on your step size (Total (Total ÷ Sample size = n)÷ Sample size = n)..
3.3. Randomly generate a Randomly generate a starting point.starting point.
4.4. Step every nStep every nthth data point data 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 the Get an alphabetical copy of the School Roll.School Roll.
2.2. Step Size = Total Step Size = Total ÷ Sample size÷ Sample size
3.3. Randomly generate a starting point.Randomly generate a starting point.
4.4. Starting from the beginning use the Starting from the beginning use the step size to pick the rest of the step size to pick the rest of the samplesample
Systematic SamplingSystematic Sampling
AdvantagesAdvantages
Cheap Cheap
Easy to Choose SampleEasy to Choose Sample
UnbiasedUnbiased
DisadvantagesDisadvantages
Needs an entire population Needs an entire population listlist
If population list is ordered If population list is ordered then sample can become then sample can become
biasedbiased
Stratified SamplingStratified Sampling
The most reliable The most reliable sampling method. sampling method.
1.1. Sort the data into strata Sort the data into strata based on information you based on information you already know.already know.
2.2. Calculate the proportions Calculate the proportions for each strata.for each strata.
3.3. Perform a Simple Random Perform a Simple Random Sample on each of the Sample on each of the strata.strata.
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 separated into year levels.separated into year levels.
2.2. Calculate the sample size for each Calculate the sample size for each year group (strata).year group (strata).
3.3. Perform a simple random sample Perform a simple random sample on each year group to their specific on each year group to their specific sample size. sample size.
Stratified SamplingStratified Sampling
Advantages Advantages
UnbiasedUnbiased
Completely Completely representative of each representative of each
of the strataof the strata
Most reliable estimatesMost reliable estimates
DisadvantagesDisadvantages
Needs entire population Needs entire population listlist
Information about entire Information about entire population needs to be population needs to be
known beforehandknown beforehand
Time consumingTime consuming
Generate a Random NumberGenerate a Random Number
1.1. Decide on the starting Decide on the starting number (in this case 1)number (in this case 1)
2.2. Decide how many you Decide how many you need (In the case of the need (In the case of the school 529 students)school 529 students)
3.3. Choose your calculatorChoose your calculator
Casio
FX-82
Casio
GraphicTexas
Random Number on a Casio Random Number on a Casio Graphics CalculatorGraphics Calculator
1.1. Decide on the starting Decide on the starting number (in this case 1)number (in this case 1)
2.2. Decide how many you Decide how many you need (In the case of the need (In the case of the school 529 students)school 529 students)
3.3. In In Run Run ModeModeIntgIntg OPTN – F6 – F4 – F5 OPTN – F6 – F4 – F5
Ran#Ran# OPTN – F6 – F3 – F4 OPTN – F6 – F3 – F4
On ScreenOn Screen
Intg(529 Intg(529 × Ran# + 1)× Ran# + 1)
Population size or Strata size Starting Value
OPTN
F3 F4 F6
( )
7 8
5 ×
+1
Intg(529 × Ran# + 1)
Random Number on a Casio FX - 82Random Number on a Casio FX - 82
1.1. Decide on the starting Decide on the starting number (in this case 1)number (in this case 1)
2.2. Decide how many you Decide how many you need (In the case of the need (In the case of the school 529 students)school 529 students)
3.3. Ran# = 2Ran# = 2ndnd function function ··
4.4. On screenOn screen
Ran# × 529 + 1 =Ran# × 529 + 1 =
notenote Ignore any decimal in the Ignore any decimal in the answeranswer
Population size or strata size
Starting value
RAN#×529+1
·
shift
Random Number on a TexasRandom Number on a Texas
1.1. Decide on the starting Decide on the starting number (in this case 1)number (in this case 1)
2.2. Decide how many you Decide how many you need (In the case of the need (In the case of the school 529 students)school 529 students)
RANDIRANDI PRB PRB →→ RANDI RANDI
,, 22ndnd Function ) Function )
3.3. On Screen On Screen RANDI(1 , 529)RANDI(1 , 529)
End ValueStarting Value
2nd
PRB
)
RANDI(1,529)
Simple Random SampleSimple Random Sample
The simplest unbiased The simplest unbiased sample. sample.
1.1. Number the entire Number the entire population.population.
2.2. Generate random Generate random numbers.numbers.
3.3. Proceed until you Proceed until you have as many as you have as many as you need ignoring any need ignoring any repeats.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 (to Number every person from 1 (to 529)529)
3.3. Generate Random numbers from 1 Generate Random numbers from 1 to the maximum you need (529).to the maximum you need (529).
4.4. Proceed until you have the desired Proceed until you have the desired sample size ignoring repeats.sample size ignoring repeats.
Strata ProportionsStrata Proportions
1.1. Number of people Number of people in strata divided by in strata divided by total in population. total in population.
2.2. Multiplied by Multiplied by number of people number of people wanted in total wanted 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 10’s115 year 10’s
3.3. Sample size of 30Sample size of 30
4.4. So year 10 sample sizeSo year 10 sample size
115 115 ÷ 529 × 30 = 6.52÷ 529 × 30 = 6.52
So take 7 year 10 studentsSo take 7 year 10 students
Systematic Step SizesSystematic Step Sizes
1.1. Number of people Number of people in population in population divided by Sample divided 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 30 Sample size of 30
3.3. So Step sizeSo Step size
529 529 ÷ 30 = 17.63333÷ 30 = 17.63333
So take every 17So take every 17thth student from the student from the starting positionstarting position
Systematic SteppingSystematic Stepping
1.1. Starting at the Starting at the random start point random start point step out till you get step 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, step Random starting point 803, step size 29size 29
2.2. 803803rdrd student on alphabetical list is student on alphabetical list is where we start.where we start.
3.3. Then 832Then 832ndnd student, 861 student, 861stst student, student, we have now reached the end of the we have now reached the end of the roll so start at the beginning 890= roll so start at the beginning 890= 1515thth student then 45 student then 45thth student… student…
MeanMean1.1. Add up all of the Add up all of the
values in the sample.values in the sample.
2.2. Divide by the sample Divide by the sample size.size.
Advantages
Easy to calculate for large samples.
Accurate and well understood
Disadvantages
Affected by outliers
Calculator Method
MedianMedian
1.1. List all the values in List 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
ModeMode
1.1. List all the values List all the values
2.2. Find the most common Find 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
Statistics on a CalculatorStatistics on a Calculator
Choose your calculatorChoose your calculator
Casio
FX-82
Casio
Graphic
Texas
1.1. In Stat ModeIn Stat Mode
2.2. In In list 1list 1 enter all data values enter all data values
3.3. In In list 2list 2 enter their enter 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 χχ is mean is mean, , χσχσn is std. devn is std. dev.).)
F2F1 F6
1Var XList :List11Var Freq :List22Var XList :List32Var YList :List42Var Freq :List5
EXIT
Statistics on a Statistics on a Casio Graphics CalculatorCasio Graphics Calculator
S.D. using table
Entering Data on Entering Data on Casio Graphics CalculatorCasio Graphics Calculator
Enter each data value in 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 don’t 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 List412345
EXE
1.1. Put your calculator into Put your calculator into statistics mode statistics mode
• Mode 2Mode 2
2.2. Clear the statistics memoryClear the statistics memory• Shift Mode 1Shift Mode 1
3.3. Enter the data carefully Enter the data carefully • 180cm M+180cm M+
4.4. Calculate desired statisticsCalculate desired statistics• Shift 2Shift 2
1.1. χχ mean mean
2.2. χσχσnn standard standard deviationdeviation
Statistics on a Statistics on a Casio FX 82 CalculatorCasio FX 82 Calculator
Scl mode clr all
1 2 3
shift mode
M+
Shown on Screen
S.D. using table
Entering Data on Entering 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 the data values as you cannot review them later to make sure that they are correct.
n =
1
M+
Statistics on a Statistics on a Texas CalculatorTexas Calculator
1.1. Put your calculator into Put your calculator into statistics modestatistics mode
1.1. 22ndnd Function DATA Function DATA
2.2. 1 - VAR1 - VAR
2.2. Enter the data carefullyEnter the data carefully 1.1. DATADATA
3.3. Calculate desired statisticsCalculate desired statistics1.1. STATVARSTATVAR
2.2. Shift between statistics with arrow Shift between statistics with arrow keyskeys1.1. nn number of number of
data valuesdata values
2.2. χχ mean mean
3.3. σχσχ standard standard deviationdeviationS.D. using table
2nd
DATA
n x Sx σx
STATVAR
Entering Data on a Entering Data on a Texas CalculatorTexas Calculator
2nd
DATA
X1 = 180
Press the Data Key to begin
Begin entering data.X1 is the data valueFollowed by the down arrow
Freq1 is that data values frequencyFollowed by the down arrowX2 is next then Freq2To check data use up arrow
DefinitionsDefinitions• PopulationPopulation The entire list of those people or things that you wish The entire list of those people or things that you wish
to sampleto sample• Census Census A survey of an A survey of an entire populationentire population• SampleSample A small group of a populationA small group of a population• Parameters Parameters Facts about an entire population Facts about an entire population gained from a censusgained from a census
(Notation: mean ‘(Notation: mean ‘μμ’ or standard deviation ‘’ or standard deviation ‘σσ’)’)• StatisticsStatistics Estimates of population parametersEstimates of population parameters calculated calculated
from a from a samplesample(Notation: mean ‘(Notation: mean ‘χχ’ or standard ’ or standard
deviation ‘s’)deviation ‘s’)• Representative Representative A sample that appears to A sample that appears to represent all elements of the represent all elements of the
in the correct proportionsin the correct proportions population population• BiasBias A sampling method that A sampling method that does not give every element of does not give every element of
the population an equal chance of selection the population an equal chance of selection
Standard DeviationStandard Deviation• This is a calculation of the This is a calculation of the
average difference between average difference between the data values and the the data values and the mean.mean.
• This measure of spread This measure of spread applies 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 Calculator to Calculate Use table to calculate
Interquartile RangeInterquartile Range1.1. Calculate the upper and Calculate the upper and
lower quartiles.lower quartiles.2.2. Upper quartile minus lower Upper quartile minus lower
quartile.quartile.3.3. This measure of spread This measure of spread
applies to the medianapplies to the median
Advantages
Well understood
Unaffected by outliers
Disadvantages
Easy to calculate for large samples.
1.1. Find the highest and lowest Find the highest and lowest value.value.
2.2. Highest value minus the Highest value minus the lowest value.lowest value.
3.3. This measure of spread This measure of spread applies to all measures of applies to all measures of centre.centre.
RangeRange
Advantages
Well understood
Unaffected by outliers
Disadvantages
Easy to calculate for large samples.
Standard Deviation by TableStandard Deviation by Table
χ χ χ – χ (χ – χ)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, doesn’t change Data values minus the Mean
Square of each of the values to the left
Final Standard Deviation is the square root of this value so s = 10
Use Calculator to Calculate
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 the Find the central value of the remaining two halves.remaining two halves.
5.5. These 2 numbers are the These 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 182so median is 181so median is 181
3.3. Discard 181 and calculate middle of Discard 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 187 187
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.
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, “If I were to repeat this sampling process, would I get the same results?”
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.
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 sample statistics? If so then I probably wouldn’t 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.
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!
Practice TasksPractice Tasks
Real Estate Stats
On Your CalculatorOn Your Calculator
In this part of the In this part of the presentation you can presentation you can check on exactly how check on exactly how to use your calculator to use your calculator effectively to help with effectively 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
Entering Data on a CalculatorEntering Data on a Calculator
Choose your calculatorChoose your calculator
Casio
FX-82
Casio
Graphic
Texas
Statistics on a CalculatorStatistics on a Calculator
Choose your calculatorChoose your calculator
Casio
FX-82
Casio
Graphic
Texas
1.1. In Stat ModeIn Stat Mode
2.2. In In list 1list 1 enter all data values enter all data values
3.3. In In list 2list 2 enter their enter 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 χχ is mean is mean, , χσχσn is std. devn is std. dev.).)
F2F1 F6
1Var XList :List11Var Freq :List22Var XList :List32Var YList :List42Var Freq :List5
EXIT
Statistics on a Statistics on a Casio Graphics CalculatorCasio Graphics Calculator
S.D. using table
Entering Data on Entering Data on Casio Graphics CalculatorCasio Graphics Calculator
Enter each data value in 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 don’t 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 List412345
EXE
1.1. Put your calculator into Put your calculator into statistics mode statistics mode
• Mode 2Mode 2
2.2. Clear the statistics memoryClear the statistics memory• Shift Mode 1Shift Mode 1
3.3. Enter the data carefully Enter the data carefully • 180cm M+180cm M+
4.4. Calculate desired statisticsCalculate desired statistics• Shift 2Shift 2
1.1. χχ mean mean
2.2. χσχσnn standard standard deviationdeviation
Statistics on a Statistics on a Casio FX 82 CalculatorCasio FX 82 Calculator
Scl mode clr all
1 2 3
shift mode
M+
Shown on Screen
S.D. using table
Entering Data on Entering 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 the data values as you cannot review them later to make sure that they are correct.
n =
1
M+
Statistics on a Statistics on a Texas CalculatorTexas Calculator
1.1. Put your calculator into Put your calculator into statistics modestatistics mode
1.1. 22ndnd Function DATA Function DATA
2.2. 1 - VAR1 - VAR
2.2. Enter the data carefullyEnter the data carefully 1.1. DATADATA
3.3. Calculate desired statisticsCalculate desired statistics1.1. STATVARSTATVAR
2.2. Shift between statistics with arrow Shift between statistics with arrow keyskeys1.1. nn number of number of
data valuesdata values
2.2. χχ mean mean
3.3. σχσχ standard standard deviationdeviationS.D. using table
2nd
DATA
n x Sx σx
STATVAR
Entering Data on a Entering Data on a Texas CalculatorTexas Calculator
2nd
DATA
X1 = 180
Press the Data Key to begin
Begin entering data.X1 is the data valueFollowed by the down arrow
Freq1 is that data values frequencyFollowed by the down arrowX2 is next then Freq2To check data use up arrow
Generate a Random NumberGenerate a Random Number
1.1. Decide on the starting Decide on the starting number (in this case 1)number (in this case 1)
2.2. Decide how many you Decide how many you need (In the case of the need (In the case of the school 529 students)school 529 students)
3.3. Choose your calculatorChoose your calculator
Casio
FX-82
Casio
GraphicTexas
Random Number on a Casio Random Number on a Casio Graphics CalculatorGraphics Calculator
1.1. Decide on the starting Decide on the starting number (in this case 1)number (in this case 1)
2.2. Decide how many you Decide how many you need (In the case of the need (In the case of the school 529 students)school 529 students)
3.3. In In Run Run ModeModeIntgIntg OPTN – F6 – F4 – F5 OPTN – F6 – F4 – F5
Ran#Ran# OPTN – F6 – F3 – F4 OPTN – F6 – F3 – F4
On ScreenOn Screen
Intg(529 Intg(529 × Ran# + 1)× Ran# + 1)
Population size or Strata size Starting Value
OPTN
F3 F4 F6
( )
7 8
5 ×
+1
Intg(529 × Ran# + 1)
Random Number on a Casio FX - 82Random Number on a Casio FX - 82
1.1. Decide on the starting Decide on the starting number (in this case 1)number (in this case 1)
2.2. Decide how many you Decide how many you need (In the case of the need (In the case of the school 529 students)school 529 students)
3.3. Ran# = 2Ran# = 2ndnd function function ··
4.4. On screenOn screen
Ran# × 529 + 1 =Ran# × 529 + 1 =
notenote Ignore any decimal in the Ignore any decimal in the answeranswer
Population size or strata size
Starting value
RAN#×529+1
·
shift
Random Number on a TexasRandom Number on a Texas
1.1. Decide on the starting Decide on the starting number (in this case 1)number (in this case 1)
2.2. Decide how many you Decide how many you need (In the case of the need (In the case of the school 529 students)school 529 students)
RANDIRANDI PRB PRB →→ RANDI RANDI
,, 22ndnd Function ) Function )
3.3. On Screen On Screen RANDI(1 , 529)RANDI(1 , 529)
End ValueStarting Value
2nd
PRB
)
RANDI(1,529)