Mean of a frequency distribution
Transcript of Mean of a frequency distribution
3.1 - 1
Example 9: Miles Run
Class Boundaries Frequency
5.5 - 10.510.5 - 15.515.5 - 20.520.5 - 25.525.5 - 30.530.5 - 35.535.5 - 40.5
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Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the mean.
3.1 - 2
Example 9: Miles Run
Class Boundaries Frequency
5.5 - 10.510.5 - 15.515.5 - 20.520.5 - 25.525.5 - 30.530.5 - 35.535.5 - 40.5
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Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the mean.
( )f xxf
3.1 - 3
Example 9: Miles Run
Class Boundaries Frequency
5.5 - 10.510.5 - 15.515.5 - 20.520.5 - 25.525.5 - 30.530.5 - 35.535.5 - 40.5
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Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the mean.
( )f xxf
Sum the frequencies
3.1 - 4
Example 9: Miles Run
Class Boundaries Frequency
5.5 - 10.510.5 - 15.515.5 - 20.520.5 - 25.525.5 - 30.530.5 - 35.535.5 - 40.5
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Below is a frequency distribution of the number of miles run per week for a sample of individuals. Find the mean.
f = 20
( )f xxf
Sum the frequencies
3.1 - 5
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.510.5 - 15.515.5 - 20.520.5 - 25.525.5 - 30.530.5 - 35.535.5 - 40.5
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f = 20
f
xfX
)( Midpoint
3.1 - 6
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.510.5 - 15.515.5 - 20.520.5 - 25.525.5 - 30.530.5 - 35.535.5 - 40.5
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( 5.5 +10.5)/2 = 8
f = 20
f
xfX
)(
3.1 - 7
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.510.5 - 15.515.5 - 20.520.5 - 25.525.5 - 30.530.5 - 35.535.5 - 40.5
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( 5.5 +10.5)/2 = 8(10.5+15.5)/2 = 13
f = 20
f
xfX
)(
3.1 - 8
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.510.5 - 15.515.5 - 20.520.5 - 25.525.5 - 30.530.5 - 35.535.5 - 40.5
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( 5.5 +10.5)/2 = 8(10.5+15.5)/2 = 13(15.5+20.5)/2 = 18
f = 20
f
xfX
)(
3.1 - 9
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.510.5 - 15.515.5 - 20.520.5 - 25.525.5 - 30.530.5 - 35.535.5 - 40.5
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( 5.5 +10.5)/2 = 8(10.5+15.5)/2 = 13(15.5+20.5)/2 = 18(20.5+25.5)/2 = 23
f = 20
f
xfX
)(
3.1 - 10
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.510.5 - 15.515.5 - 20.520.5 - 25.525.5 - 30.530.5 - 35.535.5 - 40.5
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( 5.5 +10.5)/2 = 8(10.5+15.5)/2 = 13(15.5+20.5)/2 = 18(20.5+25.5)/2 = 23(25.5+30.5)/2 = 28
f = 20
f
xfX
)(
3.1 - 11
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.510.5 - 15.515.5 - 20.520.5 - 25.525.5 - 30.530.5 - 35.535.5 - 40.5
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( 5.5 +10.5)/2 = 8(10.5+15.5)/2 = 13(15.5+20.5)/2 = 18(20.5+25.5)/2 = 23(25.5+30.5)/2 = 28(30.5+35.5)/2 = 33
f = 20
f
xfX
)(
3.1 - 12
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.510.5 - 15.515.5 - 20.520.5 - 25.525.5 - 30.530.5 - 35.535.5 - 40.5
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( 5.5 +10.5)/2 = 8(10.5+15.5)/2 = 13(15.5+20.5)/2 = 18(20.5+25.5)/2 = 23(25.5+30.5)/2 = 28(30.5+35.5)/2 = 33(35.5+40.5)/2 = 38
f = 20
f
xfX
)(
3.1 - 13
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.510.5 - 15.515.5 - 20.520.5 - 25.525.5 - 30.530.5 - 35.535.5 - 40.5
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( 5.5 +10.5)/2 = 8(10.5+15.5)/2 = 13(15.5+20.5)/2 = 18(20.5+25.5)/2 = 23(25.5+30.5)/2 = 28(30.5+35.5)/2 = 33(35.5+40.5)/2 = 38
f = 20
f ·x
f
xfX
)( Multiply each frequency by the
class midpoint
3.1 - 14
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.510.5 - 15.515.5 - 20.520.5 - 25.525.5 - 30.530.5 - 35.535.5 - 40.5
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( 5.5 +10.5)/2 = 8(10.5+15.5)/2 = 13(15.5+20.5)/2 = 18(20.5+25.5)/2 = 23(25.5+30.5)/2 = 28(30.5+35.5)/2 = 33(35.5+40.5)/2 = 38
f = 20
1×8 = 8
f ·x
f
xfX
)(
3.1 - 15
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.510.5 - 15.515.5 - 20.520.5 - 25.525.5 - 30.530.5 - 35.535.5 - 40.5
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( 5.5 +10.5)/2 = 8(10.5+15.5)/2 = 13(15.5+20.5)/2 = 18(20.5+25.5)/2 = 23(25.5+30.5)/2 = 28(30.5+35.5)/2 = 33(35.5+40.5)/2 = 38
f = 20
1×8 = 82×12 = 26
f ·x
f
xfX
)(
3.1 - 16
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.510.5 - 15.515.5 - 20.520.5 - 25.525.5 - 30.530.5 - 35.535.5 - 40.5
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( 5.5 +10.5)/2 = 8(10.5+15.5)/2 = 13(15.5+20.5)/2 = 18(20.5+25.5)/2 = 23(25.5+30.5)/2 = 28(30.5+35.5)/2 = 33(35.5+40.5)/2 = 38
f = 20
1×8 = 82×12 = 263×18 = 54
f ·x
f
xfX
)(
3.1 - 17
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.510.5 - 15.515.5 - 20.520.5 - 25.525.5 - 30.530.5 - 35.535.5 - 40.5
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( 5.5 +10.5)/2 = 8(10.5+15.5)/2 = 13(15.5+20.5)/2 = 18(20.5+25.5)/2 = 23(25.5+30.5)/2 = 28(30.5+35.5)/2 = 33(35.5+40.5)/2 = 38
f = 20
1×8 = 82×12 = 263×18 = 545×23 = 115
f ·x
f
xfX
)(
3.1 - 18
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.510.5 - 15.515.5 - 20.520.5 - 25.525.5 - 30.530.5 - 35.535.5 - 40.5
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( 5.5 +10.5)/2 = 8(10.5+15.5)/2 = 13(15.5+20.5)/2 = 18(20.5+25.5)/2 = 23(25.5+30.5)/2 = 28(30.5+35.5)/2 = 33(35.5+40.5)/2 = 38
f = 20
1×8 = 82×12 = 263×18 = 545×23 = 1154×28 = 112
f ·x
f
xfX
)(
3.1 - 19
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.510.5 - 15.515.5 - 20.520.5 - 25.525.5 - 30.530.5 - 35.535.5 - 40.5
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( 5.5 +10.5)/2 = 8(10.5+15.5)/2 = 13(15.5+20.5)/2 = 18(20.5+25.5)/2 = 23(25.5+30.5)/2 = 28(30.5+35.5)/2 = 33(35.5+40.5)/2 = 38
f = 20
1×8 = 82×12 = 263×18 = 545×23 = 1154×28 = 1123×33 = 99
f ·x
f
xfX
)(
3.1 - 20
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.510.5 - 15.515.5 - 20.520.5 - 25.525.5 - 30.530.5 - 35.535.5 - 40.5
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( 5.5 +10.5)/2 = 8(10.5+15.5)/2 = 13(15.5+20.5)/2 = 18(20.5+25.5)/2 = 23(25.5+30.5)/2 = 28(30.5+35.5)/2 = 33(35.5+40.5)/2 = 38
f = 20
1×8 = 82×12 = 263×18 = 545×23 = 1154×28 = 1123×33 = 992×38 = 76
f ·x
f
xfX
)(
3.1 - 21
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.510.5 - 15.515.5 - 20.520.5 - 25.525.5 - 30.530.5 - 35.535.5 - 40.5
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( 5.5 +10.5)/2 = 8(10.5+15.5)/2 = 13(15.5+20.5)/2 = 18(20.5+25.5)/2 = 23(25.5+30.5)/2 = 28(30.5+35.5)/2 = 33(35.5+40.5)/2 = 38
f = 20
1×8 = 82×12 = 263×18 = 545×23 = 1154×28 = 1123×33 = 992×38 = 76
f ·x
f
xfX
)(Sum the products
3.1 - 22
Example 9 Continued
Class Frequency, f Midpoint, x
5.5 - 10.510.5 - 15.515.5 - 20.520.5 - 25.525.5 - 30.530.5 - 35.535.5 - 40.5
1235432
( 5.5 +10.5)/2 = 8(10.5+15.5)/2 = 13(15.5+20.5)/2 = 18(20.5+25.5)/2 = 23(25.5+30.5)/2 = 28(30.5+35.5)/2 = 33(35.5+40.5)/2 = 38
f = 20
1×8 = 82×12 = 263×18 = 545×23 = 1154×28 = 1123×33 = 992×38 = 76
f ·x
(f ·x) = 490
f
xfX
)(
3.1 - 23
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.510.5 - 15.515.5 - 20.520.5 - 25.525.5 - 30.530.5 - 35.535.5 - 40.5
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( 5.5 +10.5)/2 = 8(10.5+15.5)/2 = 13(15.5+20.5)/2 = 18(20.5+25.5)/2 = 23(25.5+30.5)/2 = 28(30.5+35.5)/2 = 33(35.5+40.5)/2 = 38
f = 20
1×8 = 82×12 = 263×18 = 545×23 = 1154×28 = 1123×33 = 992×38 = 76
f ·x
(f ·x) = 490
20490)(
f
xfX
3.1 - 24
Example 9: Continued
Class Frequency, f Midpoint, x
5.5 - 10.510.5 - 15.515.5 - 20.520.5 - 25.525.5 - 30.530.5 - 35.535.5 - 40.5
1235432
( 5.5 +10.5)/2 = 8(10.5+15.5)/2 = 13(15.5+20.5)/2 = 18(20.5+25.5)/2 = 23(25.5+30.5)/2 = 28(30.5+35.5)/2 = 33(35.5+40.5)/2 = 38
f = 20
1×8 = 82×12 = 263×18 = 545×23 = 1154×28 = 1123×33 = 992×38 = 76
f ·x
(f ·x) = 490
5.2420490)(
f
xfX miles