btec nc - maths - statistics
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8/2/2019 BTEC NC - Maths - Statistics
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Brendan Burr BTEC National Certificate in Electronics
Statistical Methods
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8/2/2019 BTEC NC - Maths - Statistics
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Brendan Burr BTEC National Certificate in Electronics
Statistical Methods
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8/2/2019 BTEC NC - Maths - Statistics
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Brendan Burr BTEC National Certificate in Electronics
Statistical Methods
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0
1000
2000
3000
4000
5000
6000
7000
Business and
Admin
Humanities
and Social
Science
Physical and
Life Science
Technology Total
Faculty
Number of
Students
1950
2820
1050
850
Business and Admin
Humanities and Social Science
Physical and Life Science
Technology
Task 1
1.1a) Bar Chart
b) Pie Chart
8/2/2019 BTEC NC - Maths - Statistics
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Brendan Burr BTEC National Certificate in Electronics
Statistical Methods
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1.2Tally Chart
1.3
Class Interval Frequency (f)
60 - 64 4
65 - 69 11
70 - 74 18
75 - 79 16
80 - 84 7
85 - 90 4
a) Produce a histogram with a frequency polygon, for the information above:
35 l
36 ll
37 llll38 llll
39 llll ll
40 llll
41 llll
42 llll ll
43 ll
44 ll
45 l
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Brendan Burr BTEC National Certificate in Electronics
Statistical Methods
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Task 2
2.1 aCalculate for the following set of numbers:
9, 8, 7, 27, 16, 3, 1, 9, 4 and 116a) The mean = (9+8+7+27+16+3+1+9+4+116) / 10
= 20
b) The median = 1, 3, 4, 7, 8, 9, 9, 16, 27, 116= 8.5
c) The mode = 1, 3, 4, 7, 8, 9, 9, 16, 27, 116= 9
2.1 ba) The advantage of calculating the mean value is to get a round knowledgeof a number of data values. It calculates the precise centre point of all of thedataThe advantage of the median value is it can be used to calculate a typicalvalue. This means it can be used in experiments, so that if there is a massiveanomaly then the median shouldn’t be drastically altered, however with the mean it would be.The advantage of the mode is it is a true representation of the data used. Thisis because it shows the most common number used, whereas the mode isusually a decimal point and not actually the data. The mode is normally used
for calculating data on people, as there are not decimal places in humans!
b) The disadvantage of the mean is that if there is a large anomaly in ascientific experiment, then the mean would wonder a great deal, giving a falsereading to the true information gathered.The disadvantage of the median is that it is very time consuming to put all ofthe numbers in numerical order. Also if one of the middle numbers changethen the median would also change quite significantly.The disadvantage of the mode is can change very erratically. If the mode was1 and then more data was added the mode could change to completely the
other end of the scale, with just a few added numbers.
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Brendan Burr BTEC National Certificate in Electronics
Statistical Methods
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2.2a) Histogram
From this graph I can determine that the mode of the crushing strength is 9N/mm2.
b)
Cumulative Frequency Curve
0
10
20
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40
50
60
70
80
90
8.6 8.7 8.8 8.9 9 9.1 9.2 9.3
Crushing Strength (N/mm2)
C u m u l a t i v e
F r e q u e n c y
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Brendan Burr BTEC National Certificate in Electronics
Statistical Methods
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c)Mean :(8.7 x 5) + (8.8 x 9) + (8.9 x 19) + (9.0 x 25) + (9.1 x 18) + (9.2 x 4) / 80 = 8.9675
After calculating the mode, mean and median, I have come to the conclusionthat the mean would be the most accurate. This is because the mean gives thebest accuracy for the number (N/mm2) at which the material breaks down.The median on the cumulative frequency curve is difficult to mark precisely,the line may be slanted, causing an inaccuracy. It is also difficult to read fromthe graph a precise measurement, therefore an approximation must be made,causing further inaccuracy.I found the mode to be slightly inaccurate, although it is extremely close tothe mean, as it is taken from the most commonly used number. This meansthat a large amount of data can have the same value, but one piece of data canbe 1 digit greater and be declared as the mode.I also feel that the mean is more precise as it is calculated from theinformation gathered, instead of second hand data from a graph.
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Brendan Burr BTEC National Certificate in Electronics
Statistical Methods
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Bibliography
Through guidance from my lecturer, the following websites and text books Iwas able to complete this assignment:
BooksBTEC National Engineering (Mike Tooley & Lloyd Dingle)ISBN: 978-0-7506-8521-4Higher Engineering Mathematics (John Bird)ISBN: 978-0-7506-8152-0
Websiteswww.wikipedia.org
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