measure&of&average.&&&

In such circumstances as the above, a more reliable measure of average would be the Median value. This is obtained by rearranging the data into numerical order and then identifying the value at the mid-point (see right). In this case the mid-point value can be found between the 5th and 6th value when arranged in order. This is £10 and is clearly a more reliable measure of average for 9, out of 10, of these learners.

&In&such&circumstances&as&the&above,&a&more&reliable&measure&of&average&would&be&the&Median&value.&& This&is&obtained&by&rearranging&the&data&into&numerical&order&and&then&iden,fying&the&value&at&the& midHpoint&(see&right).&In&this&case&the&midHpoint&value&can&be&found&between&the&5th&and&6th&value& when&arranged&in&order.&This&is&£10&and&is&clearly&a&more&reliable&measure&of&average&for&9,&out&of&10,& of&these&learners.&&

A summary of some common ways of describing quantitative data is shown below.

! A&summary&of&some&common&ways&of&describing&quan,ta,ve&data&is&shown&below.&

Descriptive! Statistics

(Arithmetic) Mean – commonly known as the average = sum of values/number of values

Median – the middle value when all the values are arranged in order from lowest to highest

Mode – the most frequently occurring value (most appropriate when measuring the number of occurrences within a category e.g. eye colour)

Range = difference between the highest and smallest values

Interquartile Range – (a) arrange all the values in order from the lowest to the highest; (b) work out the values that lie at the ¼ and ¾ positions along the series (similar process to calculating the median, which is the value at the ½ way point) – these are the 1 between these two values – its purpose is to avoid extreme values giving a false impression of the spread of the data.

Note 1: measures of average (mean, median and mode) tell you where the bulk of the data lies - (if the average height of men is 5’7”, then most men are somewhere around this height). Note 2: measures of variance (range and interquartile range) tell you how far the data spreads around this average.

Drawing%conclusion%(from%knowledge%to%wisdom)% Drawing conclusions (from knowledge to wisdom)

You will need to draw conclusions from the knowledge you have gained from carrying out your project. This requires a thorough, critical evaluation of what your analysis of results truly indicate and whether these conclusions can be used as a reliable evidence-base for future action (e.g. to further ‘roll-out’ your intervention or to initiate further research). A central judgement to be made here will be to consider ‘can we be sure that there has been a real change/ improvement?’

You&will&need&to&draw&conclusions&from&the&knowledge&you&have&gained&from&carrying&out&your& project.&&This&requires&a&thorough,&cri,cal&evalua,on&of&what&your&analysis&of&results&truly&indicate& and&whether&these&conclusions&can&be&used&as&a&reliable&evidenceHbase&for&future&ac,on&(e.g.&to& further&‘rollHout’&your&interven,on&or&to&ini,ate&further& research).&A&central&judgement&to&be&made&here&will&be& to&consider&‘can&we&be&sure&that&there&has&been&a&real& change/improvement?’&

Consider&the&‘before&and&a\er’&results&shown&as&two& parallel&barHcharts,&to&the&le\.&It&is&clear&that&there&has& been&a&shi\&in&the&modal&average&from&‘2’&to&’4’,&but&the& range&(variability)&of&the&data&is&fairly&‘wide’&in&both& cases.&&Is&this&evidence&of&improvement&or&simply&

39

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In such circumstances as the above, a more reliable measure of average would be the Median value. This is obtained by rearranging the data into numerical order and then identifying the value at the mid-point (see right). In this case the mid-point value can be found between the 5th and 6th value when arranged in order. This is £10 and is clearly a more reliable measure of average for 9, out of 10, of these learners.

&In&such&circumstances&as&the&above,&a&more&reliable&measure&of&average&would&be&the&Median&value.&& This&is&obtained&by&rearranging&the&data&into&numerical&order&and&then&iden,fying&the&value&at&the& midHpoint&(see&right).&In&this&case&the&midHpoint&value&can&be&found&between&the&5th&and&6th&value& when&arranged&in&order.&This&is&£10&and&is&clearly&a&more&reliable&measure&of&average&for&9,&out&of&10,& of&these&learners.&&

A summary of some common ways of describing quantitative data is shown below.

! A&summary&of&some&common&ways&of&describing&quan,ta,ve&data&is&shown&below.&

Descriptive! Statistics

(Arithmetic) Mean – commonly known as the average = sum of values/number of values

Median – the middle value when all the values are arranged in order from lowest to highest

Mode – the most frequently occurring value (most appropriate when measuring the number of occurrences within a category e.g. eye colour)

Range = difference between the highest and smallest values

Interquartile Range – (a) arrange all the values in order from the lowest to the highest; (b) work out the values that lie at the ¼ and ¾ positions along the series (similar process to calculating the median, which is the value at the ½ way point) – these are the 1 between these two values – its purpose is to avoid extreme values giving a false impression of the spread of the data.

Note 1: measures of average (mean, median and mode) tell you where the bulk of the data lies - (if the average height of men is 5’7”, then most men are somewhere around this height). Note 2: measures of variance (range and interquartile range) tell you how far the data spreads around this average.

Drawing%conclusion%(from%knowledge%to%wisdom)% Drawing conclusions (from knowledge to wisdom)

You will need to draw conclusions from the knowledge you have gained from carrying out your project. This requires a thorough, critical evaluation of what your analysis of results truly indicate and whether these conclusions can be used as a reliable evidence-base for future action (e.g. to further ‘roll-out’ your intervention or to initiate further research). A central judgement to be made here will be to consider ‘can we be sure that there has been a real change/ improvement?’

You&will&need&to&draw&conclusions&from&the&knowledge&you&have&gained&from&carrying&out&your& project.&&This&requires&a&thorough,&cri,cal&evalua,on&of&what&your&analysis&of&results&truly&indicate& and&whether&these&conclusions&can&be&used&as&a&reliable&evidenceHbase&for&future&ac,on&(e.g.&to& further&‘rollHout’&your&interven,on&or&to&ini,ate&further& research).&A&central&judgement&to&be&made&here&will&be& to&consider&‘can&we&be&sure&that&there&has&been&a&real& change/improvement?’&

Consider&the&‘before&and&a\er’&results&shown&as&two& parallel&barHcharts,&to&the&le\.&It&is&clear&that&there&has& been&a&shi\&in&the&modal&average&from&‘2’&to&’4’,&but&the& range&(variability)&of&the&data&is&fairly&‘wide’&in&both& cases.&&Is&this&evidence&of&improvement&or&simply&

39

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