Statistics

*Created by Mr. Lafferty*Statisticswww.mathsrevision.comMode, Mean, Median and RangeSemi-Interquartile Range ( SIQR ) Nat 5QuartilesBoxplots Five Figure SummaryFull Standard DeviationSample Standard DeviationExam questions

Created by Mr. Lafferty

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*Created by Mr Lafferty Maths DeptStarter Questionswww.mathsrevision.com


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*Created by Mr Lafferty Maths DeptStatisticsLearning IntentionSuccess CriteriaUnderstand the terms mean, range, median and mode.We are revising the terms mean, median, mode and range.To be able to calculate mean, range, mode and median.www.mathsrevision.comAverages


*Created by Mr Lafferty Maths DeptFinding the modeThe mode or modal value in a set of data is the data value that appears the most often.For example, the number of goals scored by the local football team in the last ten games is:What is the modal score?Is it possible to have more than one modal value?Is it possible to have no modal value?YesYes2.Statisticswww.mathsrevision.comNat 5


*Created by Mr Lafferty Maths DeptThe meanThe mean is the most commonly used average.To calculate the mean of a set of values we add together the values and divide by the total number of values.For example, the mean of 3, 6, 7, 9 and 9 isStatisticswww.mathsrevision.comNat 5


*Created by Mr Lafferty Maths DeptFinding the medianThe median is the middle value of a set of numbers arranged in order. For example,Write the values in order:6,7,7,8,9,10,12.The median is the middle value.Statisticswww.mathsrevision.comNat 5


*Created by Mr Lafferty Maths DeptFinding the medianWhen there is an even number of values, there will be two values in the middle.The values in order are:There are two middle values, 47 and 51.= 49Statisticswww.mathsrevision.comNat 5


*Created by Mr Lafferty Maths DeptFinding the rangeThe range of a set of data is a measure of how the data is spread across the distribution.To find the range we subtract the lowest value in the set from the highest value. When the range is large; the values vary widely in size.When the range is small; the values are similar in size.Statisticswww.mathsrevision.comNat 5


*Created by Mr Lafferty Maths DeptHere are the high jump scores for two girls in metres.Find the range for each girls results and use this to find out who is consistently better.Joannas range = 1.62 1.15 = 0.47Kirstys range = 1.59 1.30 = 0.29The rangeStatisticswww.mathsrevision.comNat 5Kirsty is consistently better !

Joanna1.621.411.351.201.15Kirsty1.591.451.411.301.30


*Created by Mr. Lafferty Maths Dept.www.mathsrevision.comExample : This table shows the numberof light bulbs used in peoples living rooms751202512345TotalsFrequency Tables Working Out the MeanAdding a third column to this tablewill help us find the total number ofbulbs and the Mean.7 x 1 = 75 x 3 = 151 x 5 = 52 x 4 = 85 x 2 = 1045(f) x (B)Nat 5

No ofBulbs (c)Freq.(f)


*Created by Mr Lafferty Maths Dept

Now try N5 TJEx 11.1 Ch11 (page 104)www.mathsrevision.comStatisticsNat 5Averages


*Created by Mr. Lafferty*www.mathsrevision.comLesson StarterQ1.Q2.Calculate sin 90oQ3.Factorise 5y2 10yQ4.A circle is divided into 10 equal pieces.Find the arc length of one piece of the circleif the radius is 5cm. Nat 5


*Created by Mr. Lafferty Maths Dept.www.mathsrevision.comLearning IntentionSuccess CriteriaWe are learning about Quartiles.1.Understand the term Quartile.Quartiles Nat 52.Be able to calculate the Quartiles for a set of data.


*Created by Mr Lafferty Maths DeptStatisticswww.mathsrevision.comQuartiles :Splits a dataset into 4 equal lengths. Nat 5QuartilesQ1Q2Q325%50%75%Median


*Created by Mr Lafferty Maths DeptStatisticswww.mathsrevision.com Nat 5QuartilesNote : Dividing the number of values in the dataset by 4and looking at the remainder helps to identify quartiles.R1 means to can simply pick out Q2 (Median)R2 means to can simply pick out Q1 and Q3R3 means to can simply pick out Q1 , Q2 and Q3R0 means you need calculate them all


Quartiles*Created by Mr Lafferty Maths DeptStatisticswww.mathsrevision.comExample 1 :For a list of 9 numbers find the SIQR3, 3, 7, 8, 10, 9, 1, 5, 92 numbers2 numbers2 numbers2 numbersQ1Q2Q3The quartiles are Q1 :the 2nd and 3rd numbersQ2 :the 5th numberQ3 :the 7th and 8th number. Nat 51 No.3799 4 = 2 R1 1 3 3 5 7 8 9 9 10Semi-interquartile Range (SIQR) = ( Q3 Q1 ) 2 = ( 9 3 ) 2 = 3


Quartiles*Created by Mr Lafferty Maths DeptStatisticswww.mathsrevision.comExample 3 :For the ordered list find the SIQR. 3, 6, 2, 10, 12, 3, 41 number1 number1 number1 numberQ1Q2Q3The quartiles areQ1 :the 2nd numberQ2 :the 4th numberQ3 :the 6th number.7 4 = 1 R3 Nat 53410Semi-interquartile Range (SIQR) = ( Q3 Q1 ) 2 = ( 10 3 ) 2 = 3.5 2 3 3 4 6 10 12


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Now try N5 TJEx 11.2 Ch11 (page 106)www.mathsrevision.comStatisticsAverages


*Created by Mr. Lafferty*www.mathsrevision.comLesson StarterIn pairs you have 3 minutes to explain the various steps of factorising. Nat 5


*Created by Mr. Lafferty Maths Dept.www.mathsrevision.comLearning IntentionSuccess CriteriaWe are learning about Semi-Interquartile Range.1.Understand the term Semi-Interquartile Range.Semi-Interquartile Range Nat 52.Be able to calculate the SIQR.


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The range is not a good measure of spread because one extreme, (very high or very low value can have a big effect). Another measure of spread is called the Semi - Interquartile Range and is generally a better measure of spread because it is not affected by extreme values.Inter-Quartile Rangewww.mathsrevision.com


3, 4, 4, 6, 8, 8, 8, 9, 10, 10, 15, Finding the Semi-Interquartile range. 6, 3, 9, 8, 4, 10, 8, 4, 15, 8, 10Order the dataInter- Quartile Range = (10 - 4)/2 = 3 Example 1: Find the median and quartiles for the data below.


12, 6, 4, 9, 8, 4, 9, 8, 5, 9, 8, 104, 4, 5, 6, 8, 8, 8, 9, 9, 9, 10, 12Order the dataInter- Quartile Range = (9 - 5) = 1 Example 2: Find the median and quartiles for the data below.Finding the Semi-Interquartile range.


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Now try N5 TJEx 11.3 Ch11 (page 108)www.mathsrevision.comStatistics


*Created by Mr. Lafferty*www.mathsrevision.comLesson StarterIn pairs you have 3 minutes to come up with questions on

Straight Line Theory

( Remember you needed to know the answers to the questions ) Nat 5


*Created by Mr. Lafferty Maths Dept.www.mathsrevision.comLearning IntentionSuccess CriteriaWe are learning about Boxplots and five figure summary.1.Calculate five figure summary.Boxplots ( 5 figure Summary) Nat 5Be able to construct a boxplot.


Lower QuartileUpper QuartileLowest ValueHighest ValueDemo


Demo


Demo


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Now try N5 TJEx 11.4 Ch11 (page 109)www.mathsrevision.comStatisticsDemo


*Created by Mr. Lafferty Maths Dept. Starter Questionswww.mathsrevision.com Nat 5


*Created by Mr. Lafferty Maths Dept.www.mathsrevision.comLearning IntentionSuccess CriteriaKnow the term Standard Deviation.1. We are learning the term Standard Deviation for a collection of data.2.Calculate the Standard Deviation for a collection of data. Nat 5Standard DeviationFor a FULL set of Data


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*Created by Mr. Lafferty Maths Dept.www.mathsrevision.comStandard DeviationFor a FULL set of DataThe range measures spread. Unfortunately any big change in either the largest value or smallest scorewill mean a big change in the range, even though onlyone number may have changed.The semi-interquartile range is less sensitive to a single number changing but again it is only really based on two of the score.


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*Created by Mr. Lafferty Maths Dept.www.mathsrevision.comStandard DeviationFor a FULL set of DataA measure of spread which uses all the data is the

Standard Deviation

The deviation of a score is how much the score differs from the mean.


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Example 1 :Find the standard deviation of these fivescores 70, 72, 75, 78, 80.Standard DeviationFor a FULL set of DataStep 1 : Find the mean

375 5 = 75Step 3 : (Deviation)2*Created by Mr. Lafferty Maths Dept.www.mathsrevision.com-5-30350259092568Step 2 : Score - MeanStep 4 : Mean square deviation

68 5 = 13.6

Step 5 :

Take the square root of step 4

13.6 = 3.7

Standard Deviation is 3.7 (to 1d.p.)

ScoreDeviation(Deviation)27072757880Totals375


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Example 2 :Find the standard deviation of these sixamounts of money 12, 18, 27, 36, 37, 50.Standard DeviationFor a FULL set of DataStep 1 : Find the mean

180 6 = 30*Created by Mr. Lafferty Maths Dept.www.mathsrevision.comStep 2 : Score - MeanStep 3 : (Deviation)2Step 4 : Mean square deviation

962 6 = 160.33-18-12-36720324144936494000962

Step 5 :

Take the square root of step 4

160.33 = 12.7 (to 1d.p.)

Standard Deviation is 12.70

ScoreDeviation(Deviation)2121827363750Totals180


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*Created by Mr. Lafferty Maths Dept.www.mathsrevision.comStandard DeviationFor a FULL set of DataWhen Standard Deviationis LOW it means the data values are close to the MEAN.When Standard Deviationis HIGH it means the data values are spread out fromthe MEAN.MeanMean


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*Created by Mr. Lafferty Maths Dept.Now try N5 TJEx 11.5 Q1 & Q2Ch11 (page 111)

www.mathsrevision.comStandard DeviationFor a FULL set of Data


*Created by Mr. Lafferty Maths Dept. Starter Questionswww.mathsrevision.com Nat 5In pairs you have 6 mins to write down everything you know about the circle theory.Come up with a circle type of question you could be asked at National 5 Level.


*Created by Mr. Lafferty Maths Dept.www.mathsrevision.comLearning IntentionSuccess Criteria1. We are learning how to calculate the Sample Standard deviation for a sample of data.Standard DeviationFor a Sample of DataStandard deviation Nat 5Know the term Sample Standard Deviation.2.Calculate the Sample Standard Deviation for a collection of data.


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*Created by Mr. Lafferty Maths Dept.www.mathsrevision.comStandard DeviationFor a Sample of DataIn real life situations it is normal to work with a sample of data ( survey / questionnaire ). We can use two formulae to calculate the sample deviation.s = standard deviationn = number in sample = The sum ofWe will use this version because it is easier to use in practice !


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Example 1a : Eight athletes have heart rates 70, 72, 73, 74, 75, 76, 76 and 76. *Created by Mr. Lafferty Maths Dept.www.mathsrevision.comStandard DeviationFor a Sample of Data49005184532954765625577657765776x2 = 43842x = 592Step 2 :

Square all the values and find the totalStep 3 :

Use formula to calculate sample deviationStep 1 :

Sum all the valuesQ1a. Calculate the mean :592 8 = 74Q1a. Calculate the sample deviation

Heart rate (x) x27072737475767676Totals


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Created by Mr. Lafferty Maths Dept.640065616889810088369216921610000Example 1b : Eight office staff train as athletes. Their Pulse rates are 80, 81, 83, 90, 94, 96, 96 and 100 BPM*www.mathsrevision.comStandard DeviationFor a Sample of Datax = 720Q1b(ii) Calculate the sample deviationQ1b(i) Calculate the mean :720 8 = 90x2 = 65218

Heart rate (x) x280818390949696100Totals


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*Created by Mr. Lafferty Maths Dept.www.mathsrevision.comStandard DeviationFor a Sample of Data

Q1b(iii) Who are fitter the athletes or staff.Compare meansAthletes are fitter

StaffAthletes

Q1b(iv) What does the deviation tell us.Staff data is more spread out.


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*Created by Mr. Lafferty Maths Dept.Now try N5 TJEx 11.5 Q3 onwardsCh11 (page 113)

www.mathsrevision.comStandard DeviationFor a FULL set of DataAre you on Target ?I can ?Are you on Target ?I can ?Mindmap


Calculate the mean and standard deviation

Go on to next slide for part c


Qs b next slide


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