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G. D. A. Graphs, charts and tables!. L Q 1 Q 2 Q 3 H. Mean is sum of scores number of scores. Some reminders . Scores arethe wee numbers. Median isthe middle score. Mode is the score which occurs most often. Range ishighest score lowest score. - PowerPoint PPT Presentation

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Graphs, charts and tables!L Q1 Q2 Q3 H

Some reminders Median isthe middle score.Mode is the score which occurs most oftenRange ishighest score lowest scoreScores arethe wee numbers

Relative FrequencyFrequency is a measure of how often something occurs.Relative Frequency is a measure of how often something occurs compared to the total amount.Relative Frequency is given by frequency divided by the number of scores.Relative Frequency is always less than 1.

Example:A supermarket keeps a record of wine sales, noting the country of origin of each bottle. The frequency table shows one days sales.Draw a relative frequency table for the wine sales.120 24030 24027 24024 24018 24021 240= 0.5= 0.125= 0.1125= 0.1= 0.075= 0.08751Note: The total of the relative frequencies is always 1. This is a useful check.

CountryFrequencyFrance120Australia30Italy27Spain24Germany18Others21Total240

CountryFrequencyRelative FrequencyFrance120Australia30Italy27Spain24Germany18Others21Total240

If the supermarket wishes to order 1000 bottles of wine they may start by assuming that the relative frequencies are fixed Relative frequencies can be used as a measure of the likelihood of some event happening, e.g. when a customer comes in for wine, half of the time you would expect them to ask for French wine.P138/139Ex1 (omit questions 3b, 5b)French wines = 0.5 x 1000 = 500 bottlesAustralian wines = 0.125 x 1000 = 125 bottles.

Reading Pie ChartsA pie chart is a graphical representation of information. however, a pie chart can be used to calculate accurate data.Newton Wanderers have played 24 games. The pie chart shows how they got on.A full circle represents 24 games.Using a protractor we can measure the angles at the centre. (u estimate angles)15090120A full circle is 360Won: 24= 8 gamesDrawn: 24= 6 gamesLost: 24= 10 games(Check that 8 + 6 + 10 = 24)ExamplePage 140, 141Ex 2

Constructing Pie ChartsA geologist examines pebbles on a beach to study drift. She counts the types and makes a table of information. Draw a pie chart to display this information.360Now we draw the pie chart ...Example

Rock TypeFrequencyGranite43Dolerite52Sandstone31Limestone24Total150

Relative FrequencyAngle At Centre

Geology SurveyStep 1: Title.Step 2: Draw a circle.Step 3: Draw in start line.Step 4: Using a protractor draw in the other lines.1037412558(you do not need to write the angles)Step 5: Label the sectors.GraniteDoleriteSandstoneLimestoneP141/142Ex 3

Cumulative FrequencyFifty maths students are graded 1 to 10 where 10 is the best grade.The grades and frequencies are shown below.50494743372716620Cumulative FrequencyA third column has been created which keeps a running total of the frequencies.These figures are called cumulative frequencies.The cumulative frequency of grade 7 is 43.This can be interpreted as 43 candidates are graded 7 or less.P143/144Ex4Example

Cumulative Frequency DiagramsUsing the previous example we can draw a cumulative frequency diagram.We make line graph of cumulative frequency (vertical) against grade (horizontal).Maths Students Grades

GradeCumulative FrequencyUsing the diagram only How many pupils were grade 6 or less ?37At least 25 pupils were less than grade 5.P145,146 Ex 5MathsStudentsGrades

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DotplotsIt is useful to get to get a feel for the location of a data set on the number line. A good way to achieve this is to construct a dotplot. ExampleA group of athletes are timed in a 100m sprint.Their times, in seconds, are 10.8 10.9 11.2 11.5 11.6 11.6 11.6 11.9 12.2 12.2 12.8 Each piece of data becomes a data point sitting above the number line

Some features of the distribution of figures become clearer the lowest score is 10.8 secondsthe highest score is 12.8 secondsthe mode (most frequent score) is 11.6 secondsthe median (middle score) is 11.6 secondsthe distribution is fairly flat

P147/148EX 6Here are some expressions commonly used to describe distributions

The Five-Figure SummaryWhen a list of numbers is put in order it can be summarised by quoting five figures:HLQ2Q1Q3Highest numberLowest numberMedian of the full list (middle score)Lower quartile the median of the lowerhalfUpper quartile the median of the upperhalf

ExampleMake a five-figure-summary for the following data ...6 3 7 8 11 8 6 10 9 8 53 5 6 6 7 8 8 8 9 10 11L = Q1 = Q2 = Q3 = H =3 11Q2Q1Q3869

ExampleMake a five-figure-summary for the following data.6 3 7 8 11 6 10 9 8 53 5 6 6 7 8 8 9 10 11L = Q1 = Q2 = Q3 = H =311Q2Q1Q37.569

ExampleMake a five-figure-summary for the following data.6 3 7 8 11 6 10 9 53 5 6 6 7 8 9 10 11L = Q1 = Q2 = Q3 = H =311Q2Q1Q375.59.5P151: Ex 7

BoxplotsA boxplot is a graphical representation of a five-figure summary.

Example: Draw a box plot for this five-figure summary, which represents candidates marks in an exam out of 100L = Q1 = Q2 = Q3 = H =25% of the candidates got between 12 and 32(the lower whisker)50% of the candidates got between 32 and 66(in the box)25% of the candidates got between 66 and 97(the upper whisker)P152/153: Ex 8Marks out of 100

Comparing DistributionsWhen comparing two or more distributions it is (VERY) useful to consider the following the typical score (mean, median or mode) the spread of marks (the range can be used, but more often the interquartile range orsemi-interquartile range is usedMarks out of 100Interquartile range = Q3 Q1

These boxplots compare the results of two exams, one in January and one in June. Note that the January results have a median of 38 and a semi-interquartile range of 14; the June results have a median of 51 and a semi-interquartile range of 23.On average the June results are better than Januarys (since the median is higher) but scores tended to be more variable (a larger semi-interquartile range).Note the longer the box the greater the interquartile range and hence the variability.

Boxplots showing spread of marks in two successive tests.Test 1 Test 2 Mr Tennents exampleHas the class improved? (give reasons for your answer)Which would you hope to be test 1 and which test 2?

BoxplotsA boxplot is a graphical representation of a five-figure summary.

The Five-Figure SummaryWhen a list of numbers is put in order it can be summarised by quoting five figures:HHighest numberLLowest numberQ2Median of the full list (middle score)Q1Lower quartile the median of the lower halfQ3Upper quartile the median of the upper half

Example: Draw a box plot for this five-figure summary, which represents candidates marks in an exam out of 10025% of the candidates got between 12 and 32(the lower whisker)50% of the candidates got between 32 and 66(in the box)25% of the candidates got between 66 and 97(the upper whisker)Marks out of 100

ExampleMake a five-figure-summary for the following data ...6 3 7 8 11 8 6 10 9 8 53 5 6 6 7 8 8 8 9 10 11L = Q1 = Q2 = Q3 = H =3 11Q2Q1Q3869