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

1235432

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

1235432

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

1235432

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

1235432

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

1235432

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

1235432

( 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

1235432

( 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

1235432

( 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

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

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

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

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

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

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

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

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

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

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

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 = 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

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 = 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

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 = 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

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 = 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

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 = 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

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 = 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

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

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

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

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

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

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