Presentation 1.5.pptx

7/24/2019 Presentation 1.5.pptx

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1.1 Know the basics of statistics.

1.2 Understand frequency distribution.

1.3 Compute Measures of Central Tendency.

1.4 Understand cumulatie frequency distribution.

1.! Compute Measures of "ispersion for #ample.

CHAPTER 1

DESCRIPTIVE STATISTICS


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$t the end of this lesson% students should be able to&

1.!.1 Calculate mean deiation.

1.!.2 Calculate ariance.

1.!.3 Calculate standard deiation.

LEARNING OUTCOMES


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Measures of dispersion are the measures of

the de'ree of dispersion to determine how far

the alues of data in a set of data scatter or spread outfrom its aera'e alue.

(ts proide information about the distribution and

the differences between obserations in the set of data.

There are a few types of measures of dispersion&Mean "eiation

*ariance

#tandard deiation

1.5 Compute Measures of Dsperso! for Samp"e.


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$era'e of absolute differences

+differences e,pressed without plus or minus si'n-

between each alue in a set of alues%and the aera'e of all alues of that set.

1.5.1 Ca"#u"ate mea! $e%ato!.


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(s a measure of how far a set of numbers is

spread out which is how far the numbers lie

from the mean +e,pected alue-.

1.5.& Ca"#u"ate %ara!#e.


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#hows how much ariation or dispersion e,ists

from the aera'e +mean-.

(t is the square root of its ariance.

1.5.' Ca"#u"ate sta!$ar$ $e%ato!.


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ind the mean deiation% ariance and standard deiation

for the followin' data.

a- !% /% 10% 11% 11% 12% 1!% 1% 20% 22

b- 11.2% 11./% 12.0% 12.% 13.4% 14.3

E(AMPLE 1


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a- !% /% 10% 11% 11% 12% 1!% 1% 20% 22

SOLUTION 1

Mean%

Mean deiation

4.3


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a- !% /% 10% 11% 11% 12% 1!% 1% 20% 22

SOLUTION 1

#tandard deiation%

*ariance%

2.4!!!


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b- 11.2% 11./% 12.0% 12.% 13.4% 14.3

SOLUTION 1

Mean%

Mean deiation

*ariance%

#tandard deiation%


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for the frequency distribution of the data represent

the number of miles that 20 runners run durin' one wee.

E(AMPLE &

Num)er of m"es *m+ Num)er of ru!!ers

5.5 , 1-.5 1

1-.5 , 15.5 &

15.5 , &-.5 '

&-.5 , &5.5 5

&5.5 , '-.5

'-.5 , '5.5 '

'5.5 , -.5 &


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SOLUTION &

Num)er of m"es *m+ Num)er of

ru!!ers/f

Midpoint,x f . x

5.5 , 1-.5 1 8 8

1-.5 , 15.5 & 13 26

15.5 , &-.5 ' 18 54

&-.5 , &5.5 5 23 115

&5.5 , '-.5 28 112

'-.5 , '5.5 ' 33 99

'5.5 , -.5 & 38 76

f= 20 f . x = 490


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SOLUTION &

Mean%


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SOLUTION &

f x f

1 8 16.5 16.5

& 13 11.5 23.0

' 18 6.5 19.5

5 23 1.5 7.5

28 3.5 14.0

' 33 8.5 25.5

& 38 13.5 27.0

f= 20 f = 133

f x

1 8 16.5 16.5

& 13 11.5 23.0

' 18 6.5 19.5

5 23 1.5 7.5

28 3.5 14.0

' 33 8.5 25.5

& 38 13.5 27.0

f= 20


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SOLUTION &

Mean deiation


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SOLUTION &

f x f

1 8 16.5 272.25 272.25

& 13 11.5 132.25 264.50

' 18 6.5 42.25 126.75

5 23 1.5 2.25 11.25

28 3.5 12.25 49.00

' 33 8.5 72.25 216.75

& 38 13.5 182.25 364.50

f= 20 f = 1305.00

f x

1 8 16.5 272.25 272.25

& 13 11.5 132.25 264.50

' 18 6.5 42.25 126.75

5 23 1.5 2.25 11.25

28 3.5 12.25 49.00

' 33 8.5 72.25 216.75

& 38 13.5 182.25 364.50

f= 20


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SOLUTION &

*ariance%


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or 10 randomly selected colle'e students% this e,am score

frequency distribution was obtained.

ind the mean deiation% ariance and standard deiation.

E(AMPLE '

S#ore Num)er of stu$e!ts

0- , 0

00 , 1-2 22

1- , 113 43

112 , 1&5 2

1&3 4 1' /


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SOLUTION '

S#ore Num)er of

stu$e!ts/f

Midpoint,x f . x

0- , 0 94 564

00 , 1-2 22 103 2266

1- , 113 43 112 4816

112 , 1&5 2 121 3388

1&3 4 1' / 130 1170

f= 108 f . x = 12204


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SOLUTION '

Mean%


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SOLUTION '

f x f

3 94 19 114

&& 103 10 220

' 112 1 43

& 121 8 224

0 130 17 153

f= 108 f = 754

f x

3 94 19 114

&& 103 10 220

' 112 1 43

& 121 8 224

0 130 17 153

f= 108


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SOLUTION '

Mean deiation


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SOLUTION '

f x f

3 94 19 361 2166

&& 103 10 100 2200

' 112 1 1 43

& 121 8 64 1792

0 130 17 289 2601

f= 108 f = 8802

f x

3 94 19 361 2166

&& 103 10 100 2200

' 112 1 1 43

& 121 8 64 1792

0 130 17 289 2601

f= 108


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SOLUTION '

*ariance%


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for the frequency distribution of the data represent

the number of murders in 2! selected cities.

E(AMPLE

Num)er of mur$ers Num)er of #tes

' , 03 13

02 , 150 2

13- , &&& 0

&&' , &5 !

&3 , ' 1

'0 , 11 1

1& 4 2 0

25 , 5'2 1

5' , 3-- 2


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SOLUTION

Num)er of mur$ers Num)er of #tes/f Midpoint,x f . x

' , 03 13 65 845

02 , 150 2 128 256

13- , &&& 0 191 0

&&' , &5 ! 254 1270

&3 , ' 1 317 317

'0 , 11 1 380 380

1& 4 2 0 443 0

25 , 5'2 1 506 506

5' , 3-- 2 569 1138

f= 25 f . x = 4712


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SOLUTION

Mean%


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SOLUTION

f x f

1' 65 123.48 1605.24

& 128 60.48 120.96

- 191 2.52 0

5 254 65.52 327.60

1 317 128.52 128.52

1 380 191.52 191.52

- 443 254.52 0

1 506 317.52 317.52

& 569 380.52 761.04

f= 25 f = 3452.40

f x

1' 65 123.48 1605.24

& 128 60.48 120.96

- 191 2.52 0

5 254 65.52 327.60

1 317 128.52 128.52

1 380 191.52 191.52

- 443 254.52 0

1 506 317.52 317.52

& 569 380.52 761.04

f= 25


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SOLUTION

Mean deiation


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SOLUTION

f x f

1' 65 123.48 15247.31 198215

& 128 60.48 3657.83 7315.661

- 191 2.52 6.3504 0

5 254 65.52 4292.87 21464.35

1 317 128.52 16517.39 16517.39

1 380 191.52 36679.91 36679.91

- 443 254.52 64780.43 0

1 506 317.52 100819.00 100819

& 569 380.52 144795.50 289590.90

f= 25 f = 670602.20

f x

1' 65 123.48 15247.31 198215

& 128 60.48 3657.83 7315.661

- 191 2.52 6.3504 0

5 254 65.52 4292.87 21464.35

1 317 128.52 16517.39 16517.39

1 380 191.52 36679.91 36679.91

- 443 254.52 64780.43 0

1 506 317.52 100819.00 100819

& 569 380.52 144795.50 289590.90

f= 25


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SOLUTION

15.1!5/

*ariance%


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T6$7K 89U

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Presentation 1.5.pptx