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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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ind the mean deiation% ariance and standard deiation
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$e!ts/f
Midpoint,x f . x
0- , 0 94 564
00 , 1-2 22 103 2266
1- , 113 43 112 4816
112 , 1&5 2 121 3388
1&3 4 1' / 130 1170
f= 108 f . x = 12204
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SOLUTION '
Mean%
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SOLUTION '
f x f
3 94 19 114
&& 103 10 220
' 112 1 43
& 121 8 224
0 130 17 153
f= 108 f = 754
f x
3 94 19 114
&& 103 10 220
' 112 1 43
& 121 8 224
0 130 17 153
f= 108
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SOLUTION '
Mean deiation
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SOLUTION '
f x f
3 94 19 361 2166
&& 103 10 100 2200
' 112 1 1 43
& 121 8 64 1792
0 130 17 289 2601
f= 108 f = 8802
f x
3 94 19 361 2166
&& 103 10 100 2200
' 112 1 1 43
& 121 8 64 1792
0 130 17 289 2601
f= 108
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SOLUTION '
*ariance%
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ind the mean deiation% ariance and standard deiation
for the frequency distribution of the data represent
the number of murders in 2! selected cities.
E(AMPLE
Num)er of mur$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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