StatisticsStatistics

Math 314Math 314

Game PlanGame Plan

IntroductionIntroduction Presentation Presentation

Line graphLine graph Pie graphPie graph PictographPictograph Bar graphBar graph Histogram Histogram

Raw Stats Raw Stats Frequency Stats Frequency Stats Missing Values Missing Values

Stats IntroStats Intro There are lies, there are damn There are lies, there are damn

lies and then there are statistics lies and then there are statistics

- Mark - Mark TwainTwain

The gist of statistics is that you The gist of statistics is that you are trying to convey an idea by are trying to convey an idea by use of numbers. use of numbers.

It is not always honest!It is not always honest!

Stats IntroStats Intro Hypothesis: Student A has a school Hypothesis: Student A has a school

average of 10%average of 10% Conclusion: Student A is a bad Conclusion: Student A is a bad

person. person. The statistic does not measure the The statistic does not measure the

person’s goodness or badness.person’s goodness or badness. What does that statistic mean?What does that statistic mean? This means on average student A’s This means on average student A’s

mark is 10%mark is 10%

Presentation Presentation ““A picture is worth a thousand words” A picture is worth a thousand words”

- - AnonymousAnonymous

Line GraphLine Graph- time is always x - time is always x

Data t valueData t value 0 50 5 1 41 4

2 22 2 3 43 4

The Title of Your GraphThe Title of Your Graph

Time

Value

1 2 3 4 5 6 7 8-1-2

1

2

3

4

5

-1

-2

-3

-4

-5

x

y

Line Graph

Pie or CirclePie or Circle

You need to addYou need to add

to your datato your data DataData

Type # Type #

Bass 6Bass 6

Salmon 12Salmon 12

Perch 2Perch 2

TypeType ## %% AngleAngle

BassBass 66 6/20 x 100% 6/20 x 100% =30%=30%

30x3.6=130x3.6=108°08°

SalmonSalmon 1212 12/20 x12/20 x

100% =60%100% =60%60x3.6 = 60x3.6 = 216°216°

PerchPerch 22 2/20 x 2/20 x

100% =10%100% =10%10x3.6= 10x3.6= 36°36°

TotalTotal 2020 100100 360°360°

Pie ChartsPie Charts 11stst step – draw a circle step – draw a circle 22ndnd step – measure the step – measure the angleangle

33rdrd step label step label36°

108°Bass

Perch

Salmon

Do Stencil #1 & 2

PictographPictograph

Be creativeBe creative Be artisticBe artistic DataData Type # Type # Bass 6Bass 6 Salmon 12Salmon 12 Perch 2Perch 2

Legend = 2 fish

PBS

Bar Graph VerticalBar Graph Vertical

DataData Type #Type #

BassBass

SalmonSalmon

PerchPerch

0

2

4

6

8

10

12

Bass Salmon Perch

# of Fish

6122

Bar Graph HorizontalBar Graph Horizontal

DataData Type #Type #

BassBass

SalmonSalmon

PerchPerch

0

2

4

6

8

10

12

Bass Salmon Perch

# of Fish

6122

This bar graph will be tilted 90° clockwise

Compound Vertical Compound Vertical GraphGraph

DataData Type #Type #

BassBass

SalmonSalmon

PerchPerch

0

2

4

6

8

10

12

14

Bass Salmon Perch

Lake ALake B

6122

What is the same / difference here?Do #4; you have 10 minutes

HistogramHistogram A bar graph is where the bars touchA bar graph is where the bars touch Usually interested in intervals of Usually interested in intervals of

numbersnumbers Example: Given the data below, Example: Given the data below,

draw a histogram with an intervals draw a histogram with an intervals of 50of 50

(3,8,9,22,46,47,80,85,87,99)(3,8,9,22,46,47,80,85,87,99) We are thankful that they are in We are thankful that they are in

order; otherwise, put them in order!order; otherwise, put them in order!

HistogramHistogram

Interval

Tally f (frequency)

[0,50[ 6

4[50,100]

50 100

Raw Statistics (mean, Raw Statistics (mean, median,mode & Range)median,mode & Range)

Download / review slides on this Download / review slides on this topictopic

Analysis Analysis Rule #1: Put them in order 1Rule #1: Put them in order 1stst Example: Calculate the mean, mode, Example: Calculate the mean, mode,

median and range of the following…median and range of the following… (2,7,9,12,15)(2,7,9,12,15) Notice that they are in order!Notice that they are in order!

Raw Stats SolutionRaw Stats Solution

Recall #’s are (2,7,9,12,15)Recall #’s are (2,7,9,12,15) Mean = 45/9 = 9Mean = 45/9 = 9 ModeMode = 0 = 0 Median 2, 7], 9, [12, 15 = 9 Median 2, 7], 9, [12, 15 = 9 Range = 15-2 = 13Range = 15-2 = 13

Frequency StatsFrequency Stats

Data is not always simply listed out. Data is not always simply listed out. It may be presented as a frequency It may be presented as a frequency tabletable

Value xValue xi i ff

2 32 3

7 27 2

10 1 10 1

15 615 6

If we wanted to If we wanted to see it listed outsee it listed out

2,2,2,7,7,10,15,15,15,2,2,2,7,7,10,15,15,15,15,15,1515,15,15

This is not always This is not always practical!practical!

What is the mean, What is the mean, mode, median and mode, median and range of this?range of this?

ExampleExample

XXii ff xxii xx f f IntervalInterval 2 3 6 12 3 6 1stst – –

33rdrd

7 2 14 47 2 14 4thth – – 55thth

10 1 10 610 1 10 6thth

15 6 90 715 6 90 7thth – – 1212thth

Total 12 120 Total 12 120

nn sumsum

SolutionSolution

x = 120/12x = 120/12 x = 10x = 10 M M We need the (6 We need the (6thth and 7 and 7thth

interval) / 2 interval) / 2 XX66 = 10 = 10 XX77 = 15 = 15 M = M = 10 + 1510 + 15 22M = 12.5M = 12.5

SolutionSolution

Mode is the value with the biggest Mode is the value with the biggest frequencyfrequency

Mode = 15Mode = 15 Range is the highest – lowestRange is the highest – lowest Range = 15-2 = 13Range = 15-2 = 13 Another example (optional)Another example (optional)

Missing DataMissing Data These questions are given to see if These questions are given to see if

you UNDERSTAND what the you UNDERSTAND what the statistics meanstatistics mean

Tricks Tricks x = x = SUMSUM

nn Sum = x Sum = x xx n n Median: Odd / Even amount of #?Median: Odd / Even amount of #? Consider it a game – you must think!Consider it a game – you must think!

Missing DataMissing Data Example #1: Given the following Example #1: Given the following

distributions, determine the missing value(s)distributions, determine the missing value(s) 16, 23, 34, 15 n = 5 x = 3216, 23, 34, 15 n = 5 x = 32 Order 1Order 1stst! 15, 16, 23, 34! 15, 16, 23, 34 Missing 1 = AMissing 1 = A Sum = n Sum = n xx x x 5 x 32 = 160 5 x 32 = 160 Sum Sum (now)(now) = 15 + 16, + 23 + 34 = 88 160 = = 15 + 16, + 23 + 34 = 88 160 =

8888 Thus A = 160 - 88 Thus A = 160 - 88 = 72 (missing) = 72 (missing)

Missing DataMissing Data Example #2: Consider 12, 18, Example #2: Consider 12, 18,

24, 30 n = 5 and median is 2024, 30 n = 5 and median is 20 Missing 1 = AMissing 1 = A n is odd, median must be in the n is odd, median must be in the

set!set! A = 20 A = 20

Missing DataMissing Data Ex#3: 10,12,15,19,21 n=7, x=15, Median=15, Ex#3: 10,12,15,19,21 n=7, x=15, Median=15,

Mode=0 R = 16Mode=0 R = 16 Missing 2: A & BMissing 2: A & B Sum = n Sum = n xx x x 7 x 15 = 1057 x 15 = 105 Sum Sum (now)(now) = 10 + 12 + 15 + 19 + 21 = 77 = 10 + 12 + 15 + 19 + 21 = 77 Thus A + B = 105 – 77 = 28Thus A + B = 105 – 77 = 28 Median = 15 means that there is one more than Median = 15 means that there is one more than

15 and one less than 15. However, the range is 15 and one less than 15. However, the range is wrong!wrong!

Try A – B = 16 Thus, Try A – B = 16 Thus, A + B = 28 (respecting sum rule) A + B = 28 (respecting sum rule) A – B = 16A – B = 16 (respecting range) (respecting range) 2A = 442A = 44 A = 22 (missing)A = 22 (missing) B = 6B = 6