DESCRIPTIVE STATISTICS

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DESCRIPTIVE STATISTICS

• Artur Wasiak

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Table of contents

• definitions
• Why do we use descriptive statistics?
• method 1 steps of ploting histogram
• method 2 calculating statistics
• summary
• questions

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Definitions

• STATISTICS mathematical science pertaining to
  the collection, analysis, interpretation or
  explanation, and presentation of data
• DESCRIPTIVE STATISTICS statistical methods used
  to summarize or describe a collection of data

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The purpose

• Why do we use descriptive statistics?
• This is aimed at making data legible.
• Example

3,6 5,0 4,0 4,7 5,2 5,9 4,5 5,3 5,8 3,9
5,6 3,5 5,4 5,2 4,1 5,0 3,1 5,8 4,8 4,4
4,6 5,1 4,7 3,0 5,5 6,1 3,8 4,9 5,6 6,1
5,9 4,2 6,4 5,3 4,5 4,9 4,0 5,2 3,3 5,4
4,7 6,4 5,1 3,4 5,2 6,2 4,4 4,3 5,8 3,7
What do you think? Is it legible? How can we
improve it? One of the possible ways - using
graphical technics.
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Frequency distribution (1)

• We first look for the lowest and the highest
  values in the sample.

3,6 5,0 4,0 4,7 5,2 5,9 4,5 5,3 5,8 3,9
5,6 3,5 5,4 5,2 4,1 5,0 3,1 5,8 4,8 4,4
4,6 5,1 4,7 3,0 5,5 6,1 3,8 4,9 5,6 6,1
5,9 4,2 6,4 5,3 4,5 4,9 4,0 5,2 3,3 5,4
4,7 6,4 5,1 3,4 5,2 6,2 4,4 4,3 5,8 3,7
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Frequency distribution (2)

• We want to divide the data into a few groups
  called classes.
• In our example 7 classes is an appropriate number.

number of class boundaries mid-value frequency
1 2,95 3,45 3,2 ?
2 3,45 3,95 3,7 ?
3 3,95 4,45 4,2 ?
4 4,45 4,95 4,7 ?
5 4,95 5,45 5,2 ?
6 5,45 5,95 5,7 ?
7 5,95 6,45 6,2 ?
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Frequency distribution (3)
3,6(2) 5,0(5) 4,0(3) 4,7(4) 5,2(5) 5,9(6) 4,5(4) 5,3(5) 5,8(6) 3,9(2)
5,6(6) 3,5(2) 5,4(5) 5,2(5) 4,1(3) 5,0(5) 3,1(1) 5,8(6) 4,8(4) 4,4(3)
4,6(4) 5,1(5) 4,7(4) 3,0(1) 5,5(6) 6,1(7) 3,8(2) 4,9(4) 5,6(6) 6,1(7)
5,9(6) 4,2(3) 6,4(7) 5,3(5) 4,5(4) 4,9(4) 4,0(3) 5,2(5) 3,3(1) 5,4(5)
4,7(4) 6,4(7) 5,1(5) 3,4(1) 5,2(5) 6,2(7) 4,4(3) 4,3(3) 5,8(6) 3,7(2)
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Frequency distribution (4)
number of class boundaries mid-value frequency
1 2,95 3,45 3,2 4
2 3,45 3,95 3,7 5
3 3,95 4,45 4,2 7
4 4,45 4,95 4,7 9
5 4,95 5,45 5,2 12
6 5,45 5,95 5,7 8
7 5,95 6,45 6,2 5
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Histogram

• Using values from the table, we can prepare the
  histogram.

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Frequency polygone

• Connecting midpoints of the horizontal segments
  in histogram, we obtain frequency polygone.

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Calculating statistics (1)

• This is the second method of summarising
  information contained in the data.
• We can calculate statistics which characterise
  some basic features of the sample. The most
  frequently used statistics are arithmetical
  mean, variance and standard deviation, median.

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Calculating statistics (2)

• Calculating arithmetical mean
• A) using raw material(sum of 50 numbers) / 50
  4,85
• B) using frequency distribution(43,2 53,7
  56,2) / 50 4,84

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Summary

• Descriptive statistics is the first step of
  analysis of the collected data.
• There are two methods graphical technics and
  calculating statistics.
• In both of them we concede some details to make
  the whole set of data legible.

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THE END

• Any questions?
• THANK YOU!!!
• The presentation can be downloaded from
  http//arturwasiak.republika.pl/studia/descriptive
  _statistics.ppt