The Use Of Statistics
There Are Two Branches Of Statistics Descriptive
statistics refers to the methods for SUMMERAZING information so that the information is more useful or can be obtained communicative or effective
4 Examples Of DISCRIPTIVE Statistic: FRENQUECY Table Percent Distribution Bar Graph Pie Chart
Inferential Statistics Refers
to the procedure used to make GENERALIZATIION from a sample to the larger population from which the sample was drawn There are two DIFFENT types of MESUREMENTS
Two Types Of Measurements: Measure
of central tendency which gives us information about the “center” of the way data is distributed Mean Mode Median
Measurement
dispersion
of
Sample Questions How
many people in your family, other than you, have attended college? How many people in your family have graduated from college? What is your grade point average (G.P.A)? Do you have a part time or full time or no job?
How Many People in Your Family Graduated From College ? Descriptive
statistics Sample numbers: 0, 0,0,0,0,0,0,0,0,1,1, 1,1,1,2,2,2,2,2,2,3, 3,3,4,6
Frequency Bar
graph Pie chart
table
Frequency Table Category Tally
Frequen cy 9
Percent
0
///// ////
37.5%
1
/////
5
20.8%
2
///// /
6
25%
3
//
2
8.3%
4
/
1
4.2%
6
/
1
4.2%
9 8 .
7
.
6
.
5
.
4
. .
3
.
2
..
1
.
0 0
1
2
3
4
6
Pie Chart
37.5 20.8 25 8.3 4.2 4.2
Do You Have a Part Time or Full Time or No Job?
Do You Have A Part Time Full Time or No Job? Categorie Tally s
Frequency percent
No job
///// /
6
22.22%
Part time job
///// /////
10
37.04%
Full time job
///// ///// /
11
40.74%
Do You Have A Part Time or Full Time or No Job? 45.00% 40.00% 35.00% 30.00% 25.00% 20.00% 15.00% 10.00% 5.00% 0.00%
No J ob Part time job Full time job
Bar Graph
No J ob Part Time J ob Full Time J o Slice 4
How Many People in Your Family Other Than You Attended College
Descriptive
statistics Sample numbers: 5,3,0,2,1,5,2,0,1,2, 2,1,1,1,1,1,2,3,2,1, 4,2,1,3,2,2
Frequency table Bar graph Pie chart
Frequency Table Category
Tally
Frequency Percent
0
//
2
7.7
1
///// ////
9
34.6
2
///// ////
9
34.6
3
///
3
11.5
4
/
1
3.8
5
//
2
7.7
Bar Graph 35.00% 30.00% 25.00% 20.00%
3-D Column 1 3-D Column 2 3-D Column 3
15.00% 10.00% 5.00% 0.00%
0
1
2
3
4
5
Bar Graph 0 1 2 3 4 5
Inferential Statistics Mean Median Mode Range Sample
numbers 0,0,1,1,1,1,1,1,1,1, 1,2,2,2,2,2,2,2,2,2, 3,3,3,4,5,5.
Inferential Statistics Mean=
68/26=2.62 Median= 2+2/2=4/2=2 Mode = 1,2 Range =0+5/2= 2
Xi 0
Xi –X 0-2.6
0
0-2.6
1
1-2.6
1
1-2.6
1
1-2.6
1
1-2.6
1
1-2.6
1
1-2.6
1
1-2.6
1
1-2.6
1
1-2.6
(Xi –X)^2 (-2.6) ^2=6.76 (-2.6) ^2=6.76 (-1.6) ^2=2.56 (-1.6) ^2=2.56 (-1.6) ^2=2.56 (-1.6) ^2=2.56 (-1.6) ^2=2.56 (-1.6) ^2=2.56 (-1.6) ^2=2.56 (-1.6) ^2=2.56 (-1.6) ^2=2.56
Xi 2 2 2 2 2 2 2 2 2 3 3 3
Xi-X 2-2.6 2-2.6 2-2.6 2-2.6 2-2.6 2-2.6 2-2.6 2-2.6 2-2.6 3-2.6 3-2.6 3-2.6
(Xi-X)^2 (-.6 )^2=.36 (-.6)^2=.36 (-.6)^2=.36 (-.6)^2=.36 (-.6)^2=.36 (-.6)^2=.36 (-.6)^2=.36 (-.6)^2=.36 (-.6)^2=.36 (-.4)^2=.16 (-.4)^2=.16 (-.4)^2=.16
Xi
Xi-X
(Xi-X)^2
4
4-2.6
(1.4)^2=1.96
5
4-2.6
(2.4)^2=5.76
5
5-2.6
(2.4)^2=5.76
Standard Deviation S^2=(Xi-X)^2/ 53.76/26
n
=2.1 Take the square root of the number=1.44 The distance that one is from the mean.
What Is Your Grade Point Average? •Excellent •Good •Average •Poor
What Is Your Grade Point Average? Raw
data:2.1,2.1,2.4, 2.4,2.5,2.5,2.6,2.7, 2.7,2.7,2.7,2.8,2.8, 2.9,3.0,3.0,3.1,3.1, 3.2,3.3,3.5,3.5,3.6, 3.8,4.0
Descriptive
statistics Inferential statistics
Frequency Table Categorie Tally s
Frequency Percent
4.0-3.5
/////
5
20%
3.49-2.5
///// ///// ///// ///
18
72%
2.4-1.5
//
2
8%
Bar Graph 80% 70% 60% 50% 3-D Column 1 . .
40% 30% 20% 10% 0%
4.0-3.5
3.49-2.5
2.4-1.5
Pie Chart
4.0-3.5 3.49-2.5 2.4-1.5 Slice 4
Inferential Statistics =Xi/n=2.9 Mode= 2.8 Median=2.7 Mean
Xi 2.1 2.1 2.4 2.4 2.5 2.5 2.6 2.7 2.7 2.7 2.7 2.8
Xi-X 2.1-2.9 2.1-2.9 2.4-2.9 2.4-2.9 2.5-2.9 2.5-2.9 2.6-2.9 2.7-2.9 2.7-2.9 2.7-2.9 2.7-2.9 2.8-2.9
(Xi-X)^2 (-.8)^2=.64 (-.8)^2=.64 (-.5)^2=.25 (-.5)^2=.25 (-.4)^2=.16 (-.4)^2=.16 (-.3)^2=.9 (-.2)^2=.4 (-.2)^2=.4 (-.2)^2=.4 (-.2)^2=.4 (-.1)^2=.1
2.8 2.9 3.0 3.0 3.1 3.1 3.2 3.3 3.5 3.5 3.6 3.8 4.0
2.1-2.8 2.1-2.9 3.0-2.9 3.0-2.9 3.1-2.9 3.1-2.9 3.2-2.9 3.3-2.9 3.5-2.9 3.5-2.9 3.6-2.9 3.8-2.9 4.0-2.9
(-.1)^2=.1 (0)^2=0 (.1)^2=.1 (.1)^2=.1 (.2)^2=.4 (.2)^2=.4 (.3)^2=.9 (.4)^2=.16 (.6)^2=.36 (.6)^2=.36 (1)^2=1 (.9)^2=.81 (1.1)^2=1.21