Statistics - PowerPoint PPT Presentation

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Statistics

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Statistics Math 314 – PowerPoint PPT presentation

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Title: Statistics


1
Statistics
  • Math 314

2
Game Plan
  • Introduction
  • Presentation
  • Line graph
  • Pie graph
  • Pictograph
  • Bar graph
  • Histogram
  • Raw Stats
  • Frequency Stats
  • Missing Values

3
Stats Intro
  • There are lies, there are damn lies and then
    there are statistics
  • - Mark Twain
  • The gist of statistics is that you are trying to
    convey an idea by use of numbers.
  • It is not always honest!

4
Stats Intro
  • Hypothesis Student A has a school average of 10
  • Conclusion Student A is a bad person.
  • The statistic does not measure the persons
    goodness or badness.
  • What does that statistic mean?
  • This means on average student As mark is 10

5
Presentation
  • A picture is worth a thousand words
  • - Anonymous
  • Line Graph
  • - time is always x
  • Data t value
  • 0 5
  • 1 4
  • 2 2
  • 3 4

6
Line Graph
7
Pie or Circle
Type Angle
Bass 6 6/20 x 100 30 30x3.6108
Salmon 12 12/20 x 100 60 60x3.6 216
Perch 2 2/20 x 100 10 10x3.6 36
Total 20 100 360
  • You need to add
  • to your data
  • Data
  • Type
  • Bass 6
  • Salmon 12
  • Perch 2

8
Pie Charts
  • 1st step draw a circle
  • 2nd step measure the angle
  • 3rd step label

Bass
108
36
Salmon
Do Stencil 1 2 ?
Perch
9
Pictograph
  • Be creative
  • Be artistic
  • Data
  • Type
  • Bass 6
  • Salmon 12
  • Perch 2

P
B
S
Legend 2 fish
10
Bar Graph Vertical
  • Data
  • Type
  • Bass
  • Salmon
  • Perch

6
12
2
11
Bar Graph Horizontal
  • Data
  • Type
  • Bass
  • Salmon
  • Perch

6
12
2
This bar graph will be tilted 90 clockwise
12
Compound Vertical Graph
  • Data
  • Type
  • Bass
  • Salmon
  • Perch

6
12
2
What is the same / difference here?
Do 4 you have 10 minutes ?
13
Histogram
  • A bar graph is where the bars touch
  • Usually interested in intervals of numbers
  • Example Given the data below, draw a histogram
    with an intervals of 50
  • (3,8,9,22,46,47,80,85,87,99)
  • We are thankful that they are in order
    otherwise, put them in order!

14
Histogram
Interval
Tally
f (frequency)
0,50
6
4
50,100
50
100
15
Raw Statistics (mean, median,mode Range)
  • Download / review slides on this topic
  • Analysis
  • Rule 1 Put them in order 1st
  • Example Calculate the mean, mode, median and
    range of the following
  • (2,7,9,12,15)
  • Notice that they are in order!

16
Raw Stats Solution
  • Recall s are (2,7,9,12,15)
  • Mean 45/9 9
  • Mode 0
  • Median 2, 7, 9, 12, 15 9
  • Range 15-2 13

17
Frequency Stats
  • Data is not always simply listed out. It may be
    presented as a frequency table
  • Value xi f
  • 2 3
  • 7 2
  • 10 1
  • 15 6
  • If we wanted to see it listed out
  • 2,2,2,7,7,10,15,15,15,15,15,15
  • This is not always practical!
  • What is the mean, mode, median and range of this?

18
Example
Xi f xi x f Interval
  • 2 3 6 1st 3rd
  • 7 2 14 4th 5th
  • 10 1 10 6th
  • 15 6 90 7th 12th
  • Total 12 120

n
sum
19
Solution
  • x 120/12
  • x 10
  • M ? We need the (6th and 7th interval) / 2
  • X6 10
  • X7 15
  • M 10 15
  • 2
  • M 12.5

20
Solution
  • Mode is the value with the biggest frequency
  • Mode 15
  • Range is the highest lowest
  • Range 15-2 13
  • Another example (optional)

21
Missing Data
  • These questions are given to see if you
    UNDERSTAND what the statistics mean
  • Tricks ? x SUM
  • n
  • Sum x x n
  • Median Odd / Even amount of ?
  • Consider it a game you must think!

22
Missing Data
  • Example 1 Given the following distributions,
    determine the missing value(s)
  • 16, 23, 34, 15 n 5 x 32
  • Order 1st! 15, 16, 23, 34
  • Missing 1 A
  • Sum n x x
  • 5 x 32 160
  • Sum (now) 15 16, 23 34 88 160 88
  • Thus A 160 - 88
  • 72 (missing)

23
Missing Data
  • Example 2 Consider 12, 18, 24, 30 n 5 and
    median is 20
  • Missing 1 A
  • n is odd, median must be in the set!
  • A 20

24
Missing Data
  • Ex3 10,12,15,19,21 n7, x15, Median15,
    Mode0 R 16
  • Missing 2 A B
  • Sum n x x
  • 7 x 15 105
  • Sum (now) 10 12 15 19 21 77
  • Thus A B 105 77 28
  • Median 15 means that there is one more than 15
    and one less than 15. However, the range is
    wrong!
  • Try A B 16 Thus,
  • A B 28 (respecting sum rule)
  • A B 16 (respecting range)
  • 2A 44
  • A 22 (missing)
  • B 6
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