Download Sect. 3.3 Measures of Spread

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3.3 Measures of Spread
Date __________
Measures of Spread
The terms spread, dispersion, and variation all refer to a measure of the way a data set is distributed
about some central value. These measures will give us another numerical value that will allow us to
describe a data set.
Range is the difference between the maximum value and the minimum value in the data set. It
can be really large if there are outlier values.
Interquartile range is the difference between Q1 and Q3. The smaller the range, the more
consistent the data values are.
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3.3 Measures of Spread
Date __________
Deviation - the difference between a data value and the mean.
_
Deviation= xi  x
Variance (  2 ) – a measure of dispersion that is found by averaging the square of the deviation of
each piece of data
Standard Deviation – a measure of dispersion found by taking the square root of the variance.
The Greek letter (  2 ) sigma is used to represent variance and standard deviation,  .
Standard Deviation (Ungrouped Data)

 (x
_
i
 x) 2
n
Standard Deviation (Grouped Data)
For grouped data, the formula is revised by multiplying the group deviation by its frequency.


_
f i ( xi  x) 2
n
MDM4U
3.3 Measures of Spread
Date __________
Ex. 2 Ten people were tested to determine their preferred decibel level when listening to music. These are the
results:
78 96 83 86 105 82 101 71 92 99
Calculate the IQR and standard deviation.
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3.3 Measures of Spread
Date __________
Ex. 3 A railway line give out small bags of peanuts to its travellers, and each bag does not always contain the
same number of peanuts. The following table represents a sample of 31 bags showing the number of peanuts
per bag.
Number of Peanuts
Frequency
28
2
29
5
30
10
a) Calculate the mean number of peanuts per bag.
b) Calculate the standard deviation for this sample.
31
9
32
4
33
1