BTEC NC - Maths - Statistics

8/2/2019 BTEC NC - Maths - Statistics

http://slidepdf.com/reader/full/btec-nc-maths-statistics 1/8

Brendan Burr BTEC National Certificate in Electronics

Statistical Methods

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Statistical Methods

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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




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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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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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

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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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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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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

Documents

BTEC NC - Maths - Statistics