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