This page contains a Flash digital edition of a book.
When&we&use&the&term&‘average’&in&general& speech,&we&tend&to&think&about&the&formula&that& we&most&likely&learnt&at&school&H&this&is&correctly& known&as&the&Arithme,c&Mean&(or&just&‘Mean).&&


Learner


There&are&two&circumstances&when&this&measure&of&average&is&either&not&feasible&or&inappropriate.&& The&first&circumstance&is&where&you&have&collected&and& grouped&qualita,ve&data&and&your&analysis&has&produced& simple&counts&(or&‘frequencies’)&of&responses&within&a& series&of&categories.&Consider,&for&example,&the&chart&to& the&right.&&It&would&not&be&possible&or&meaningful&to& calculate&an&arithme,c&mean&of&this&data&because&you& would&have&to&add&together&qualita,vely&different&subH sets&of&data.&&(If&we&have&10&apples&and&5&pears,&would&it&


Guide7&to&Qualita,ve&and&Quan,ta,ve&Analysis 8


1 2 3 4 5 6


£120.00 £5.00


£0.00 9 10 Total Mean


£10.00 £15.00


£20.00


Pocket%Money £8.00 £7.50


£10.00 £12.50 £12.00


There are two circumstances when this measure of average is either not feasible or inappropriate. The first circumstance is where you have collected and grouped qualitative data and your analysis has produced simple counts (or ‘frequencies’) of responses within a series of categories. Consider, for example, the chart to the right. It would not be possible or


be&meaningful&to£200.00&say&we&have&an&average&of&7.5&apple/pears?).&In&this&situa,on,&you&would&use&a& measure&of&average&known&as&the&Mode,&which&is&simply&the&most&frequently&occurring&category& within&the&set&of&data&……&in&this&case,&‘career&development’&which&rYeceived&22&responses.&


The&second&circumstance&is&where&your&quan,ta,ve&data&includes&some&occurrences&of&unreliably& extreme&data.&&Imagine&you&survey&20&learners&to&find&out&how&much&pocket&money&they&receive,&at& home,&with&the&results&as&depicted&in&the&table&to&the&le\.&


You&may&no,ce&from&this&data&(raw&results)&table&that&9&out&of&the&10&learner’s&pocket&money&is&less& than&£15&and&most&of&it&being&below&£12.50&–&yet&the&arithme,c&mean&is&£20.&&In&this&situa,on&the& mean&is&not&a&reliable&indicator&of&the&average&amount&received&by&these&10&learners&and&this&is& because&Learner&6&has&par,cularly&wealthy&parents&and&a&weekly&pocket&money&allowance&of&£120.&& These&is&clearly&a&rela,vely&extreme&value&for&the&general&demographic&of&learners&in&the&group&and& such&extreme&values&tend&to&make&the&arithme,c&mean&unreliable&&as&a&&&


There&are&two&circumstances&when&this&measure&of&average&is&either&not&feasible&or&inappropriate.&& The&first&circumstance&is&where&you&have&collected&and& grouped&qualita,ve&data&and&your&analysis&has&produced& simple&counts&(or&‘frequencies’)&of&responses&within&a& series&of&categories.&Consider,&for&example,&the&chart&to& the&right.&&It&would&not&be&possible&or&meaningful&to& calculate&an&arithme,c&mean&of&this&data&because&you& would&have&to&add&together&qualita,vely&different&subH sets&of&data.&&(If&we&have&10&apples&and&5&pears,&would&it&


be&meaningful&to&say&we&have&an&average&of&7.5&apple/pears?).&In&this&situa,on,&you&would&use&a& measure&of&average&known&as&the&Mode,&which&is&simply&the&most&frequently&occurring&category& within&the&set&of&data&……&in&this&case,&‘career&development’&which&received&22&responses.&


The&second&circumstance&is&where&your&quan,ta,ve&data&includes&some&occurrences&of&unreliably& extreme&data.&&Imagine&you&survey&20&learners&to&find&out&how&much&pocket&money&they&receive,&at& home,&with&the&results&as&depicted&in&the&table&to&the&le\.&


You&may&no,ce&from&this&data&(raw&results)&table&that&9&out&of&the&10&learner’s&pocket&money&is&less& than&£15&and&most&of&it&being&below&£12.50&–&yet&the&arithme,c&mean&is&£20.&&In&this&situa,on&the& mean&is&not&a&reliable&indicator&of&the&average&amount&received&by&these&10&learners&and&this&is& because&Learner&6&has&par,cularly&wealthy&parents&and&a&weekly&pocket&money&allowance&of&£120.&& These&is&clearly&a&rela,vely&extreme&value&for&the&general&demographic&of&learners&in&the&group&and& such&extreme&values&tend&to&make&the&arithme,c&mean&unreliable&&as&a&&&


The second circumstance is where your quantitative data includes some occurrences of unreliably extreme data. Imagine you survey 20 learners to find out how much pocket money they receive, at home, with the results as depicted in the table to the left. You may notice from this data (raw results) table that 9 out of the 10 learner’s pocket money is less than £15 and most of it being below £12.50 – yet the arithmetic mean is £20. In this situation the mean is not a reliable indicator of the average amount received by these 10 learners and this is because Learner 6 has particularly wealthy parents and a weekly pocket money allowance of £120. These is clearly a relatively extreme value for the general demographic of learners in the group and such extreme values tend to make the arithmetic mean unreliable as a measure of average.


Guide&to&Q6ualita,ve&and&Quan Total


2nd 3rd 4th 5th 6th 7th 8th 9th


10th Mean measure&of&average.&&&


&In&such&circumstances&as&the&above,&a&more&reliab This&is&obtained&by&rearranging&the&data&into&nume midHpoint&(see&right).&In&this&case&the&midHpoint&va when&arranged&in&order.&This&is&£10&and&is&clearly&a of&these&learners.&&


38 10


£10.00 £10.00 £12.00 £12.50 £15.00


£120.00


£200.00 £20.00


Order Learner 1st


8 7 2 1 3 9 5 4


Pocket%Money £0.00 £5.00 £7.50 £8.00


average of 7.5 apple/pears?). In this situation, you would use a measure of average known as the Mode, which is simply the most frequently occurring category within the set of data. In this case, the mode is ‘career development’ which received 22 responses.


meaningful to calculate an arithmetic mean of this data because you would have to add together qualitatively different sub-sets of data. (If we have 10 apples and 5 pears, would it be meaningful to say we have an


Average&=&Total&(of&a&set&of&scores)& &&&&&&&&&&&&&&&&&&&&&&n&&&&&(number&of&scores&in&the&set)&&&&&&


There&are&two&circumstances&when&this&measure& The&first&circumstance&is&where&you&have&collecte grouped&qualita,ve&data&and&your&analysis&has&pr simple&counts&(or&‘frequencies’)&of&responses&with series&of&categories.&Consider,&for&example,&the&ch the&right.&&It&would&not&be&possible&or&meaningful calculate&an&arithme,c&mean&of&this&data&because would&have&to&add&together&qualita,vely&differen sets&of&data.&&(If&we&have&10&apples&and&5&pears,&w


be&meaningful&to&say&we&have&an&average&of&7.5&a measure&of&average&known&as&the&Mode,&which&is within&the&set&of&data&……&in&this&case,&‘career&dev


The&second&circumstance&is&where&your&quan,ta, extreme&data.&&Imagine&you&survey&20&learners&to home,&with&the&results&as&depicted&in&the&table&to


ou&may&no,ce from&this&data&(raw&results)&table& than&£15&and&most&of&it&being&below&£12.50&–&yet mean&is&not&a&reliable&indicator&of&the&average&am because&Learner&6&has&par,cularly&wealthy&paren These&is&clearly&a&rela,vely&extreme&value&for&the such&extreme&values&tend&to&make&the&arithme,c


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