QMB-210 Lecture Notes - Lecture 7: Federazione Industria Musicale Italiana, Percentile, Standard Deviation

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1
Sarah Welsh
QMB 210
Nisar
February 1, 2017
Chapter 3
The mean of grouped data
Find the mid-point
o What is halfway between each class
Multiply by the frequency
Add them up
Divide by the total of the frequency
8.5
32
272
410126
(4)(15)(10)(11)(12)(7)(6)(3) ==
+++
+++
=»
å
=
n
mf
x
k
i
ii
1
Sample variance
Midpoint, minus mean, squared, multiplied by the frequency
Divide by the total number of frequency
o THEN minus one
1.419
31
440
14)1012(6
(4)8.5)(15(10)8.5)(11(12)8.5)(7(6)8.5)(3
2222
==
-+++
-+-+-+-
=
-
-
»
å
=
1
1
2
2
n
f)xm(
s
k
i
ii
This gives you variance
Standard deviation is the square root of variance
Population variance
Sae but do’t ius 
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2
******************************************************************************
Pg. 115
3.29
Values Frequency
0-2 4
2-4 2
4-6 9
6-8 7
A) Calculate the approximate mean ( ) of these sample data
(1x4)+(3x2)+(5x9)+(7x7)
4+2+9+7 = 4.73
B) Calculate the approximate standard deviation of these sample data
(1-4.73)^2 (4)+ (3-4.73)^2 (2)+ (5-4.73)^2 (9)+ (7-4.73)^2 (7) 98.38
(4+2+9+7)-1 = 21 = 4.68
o So, 4.68 is the variance. Standard deviation is the square root of this. 2.16
******************************************************************************
Percentiles
Measure the approximate percentage of values in the data set that are below the value
of interest
o Examples:
o 20% of the data values are below the 20th percentile
o 73% of the data values are below the 73rd percentile
Always round the number up
)(
100
n
p
i=
o p = the percentile of interest
o n = the number of data values
E.g (Ch. 3 Slide 60)
1
33
2
56
3
61
4
65
5
67
6
88
x
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