Calculating the mode

System
System Posts: 100,534 🤖 Admin 🤖
edited June 18 in AAT student discussion
I am working through reports and returns and have come accross the following question which i just dont get.<BR>Litres of fuel Frequency<BR><800 1 <BR>800<1000 3<BR>1000<1200 11<BR>1200<1400 22<BR>1400<1600 24<BR><BR>Using the formula (F1-F0)xC/2F1-F0-F2 +L<BR>Calculate the mode of the fuel usage.<BR><BR>L= Lower limit of model class<BR>F0= Frequency of next class below model class<BR>F1= Frequency of model class<BR>F2= Frequency of next class above model class<BR>C=Width of model class<BR><BR>I thought the mode was as simple as the most frequently occuring amount and therefore 24 vehicles use 1400 to 1600 would be the mode.<BR><BR>But using this formula is throwing me completely. <BR>Can anyone explain this further.<BR>thanks

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  • System
    System Posts: 100,534 🤖 Admin 🤖
    Calculating the mode

    Mode means you are looking for a value<BR>You have found the most common class but not the most common value<BR>On a histogram you would no doubt draw some lines and find the modal value, but without a graph you are left with a formula which does the same thing<BR>Here the modal class is 1400-1600 (F1) 24<BR>There is no frequency for a class above this so F2 is 0<BR>F0 is the class below 1200-1400 22<BR><BR>and the width of each class is 200<BR><BR>We know the mode is somewhere between 1400 and 1600 so the difference will be added to 1400 (the lower limit of the modal class)<BR>F1-F0 .........24-22...then multiply by the width of the class 200=...400<BR><BR>2F1-F0-F2 (ie. double the modal class and deduct the classes immediately above and below)<BR>48-22-0...= 26<BR><BR>So our value will be 400/26 more than the lower limit of the modal class (1400)<BR><BR>1415.4<BR><BR>Does it look reasonable? well yes we would certainly expect a value well below the mid-point 1500 as there are no values greater than those in this class, Added to this the class below the modal class has a frequency of 22 which is nearly as much as the modal class so something in the region 1400-1425 would be sensible<BR><BR>In this case 1415 looks as if it is the right answer based on the distribution. <BR><BR>sandy.hood@chichester.ac.uk
  • System
    System Posts: 100,534 🤖 Admin 🤖
    Calculating the mode

    Thanks Sandy.<BR><BR>When I went away and thought about it more I was kind of getting to your point.<BR><BR>Karen<BR>

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