2. Statistics Math 314

3. Game Plan Introduction Introduction Presentation Presentation Line graph Line graph Pie graph Pie graph Pictograph Pictograph Bar graph Bar graph Histogram Histogram Raw Stats Raw Stats Frequency Stats Frequency Stats Missing Values Missing Values

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

5. Stats Intro Hypothesis: Student A has a school average of 10% Hypothesis: Student A has a school average of 10% Conclusion: Student A is a bad person. Conclusion: Student A is a bad person. The statistic does not measure the person’s goodness or badness. The statistic does not measure the person’s goodness or badness. What does that statistic mean? What does that statistic mean? This means on average student A’s mark is 10% This means on average student A’s mark is 10%

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

7. The Title of Your Graph Time Value Line Graph

8. Pie or Circle You need to add You need to add to your data Data Data Type # Type # Bass 6 Bass 6 Salmon 12 Salmon 12 Perch 2 Perch 2 Type#%Angle Bass6 6/20 x 100% =30% 30x3.6=108° Salmon12 12/20 x 100% =60% 60x3.6 = 216° Perch2 2/20 x 100% =10% 10x3.6= 36° Total20100360°

9. Pie Charts 1 st step – draw a circle 1 st step – draw a circle 2 nd step – measure the angle 2 nd step – measure the angle 3 rd step label 3 rd step label 36° 108° Bass Perch Salmon Do Stencil #1 & 2

10. Pictograph Be creative Be creative Be artistic Be artistic Data Data Type # Type # Bass 6 Bass 6 Salmon 12 Salmon 12 Perch 2 Perch 2 Legend = 2 fish P B S

11. Bar Graph Vertical Data Data Type # Type # Bass Bass Salmon Salmon Perch Perch 6 12 2

12. Bar Graph Horizontal Data Data Type # Type # Bass Bass Salmon Salmon Perch Perch 6 12 2 This bar graph will be tilted 90° clockwise

13. Compound Vertical Graph Data Data Type # Type # Bass Bass Salmon Salmon Perch Perch 6 12 2 What is the same / difference here? Do #4; you have 10 minutes

14. Histogram A bar graph is where the bars touch A bar graph is where the bars touch Usually interested in intervals of numbers Usually interested in intervals of numbers Example: Given the data below, draw a histogram with an intervals of 50 Example: Given the data below, draw a histogram with an intervals of 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 order; otherwise, put them in order! We are thankful that they are in order; otherwise, put them in order!

15. Histogram IntervalTally f (frequency) [0,50[6 4 [50,100] 50100

16. Raw Statistics (mean, median,mode & Range) Download / review slides on this topic Download / review slides on this topic Analysis Analysis Rule #1: Put them in order 1 st Rule #1: Put them in order 1 st Example: Calculate the mean, mode, median and range of the following… Example: Calculate the mean, mode, 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!

17. Raw Stats Solution Recall #’s are (2,7,9,12,15) Recall #’s are (2,7,9,12,15) Mean = 45/9 = 9 Mean = 45/9 = 9 Mode = 0 Mode = 0 Median 2, 7], 9, [12, 15 = 9 Median 2, 7], 9, [12, 15 = 9 Range = 15-2 = 13 Range = 15-2 = 13

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

19. Example X i f x i x f Interval X i f x i x f Interval 2 3 6 1 st – 3 rd 2 3 6 1 st – 3 rd 7 2 14 4 th – 5 th 7 2 14 4 th – 5 th 10 1 10 6 th 10 1 10 6 th 15 6 90 7 th – 12 th 15 6 90 7 th – 12 th Total 12 120 nsum

20. Solution x = 120/12 x = 120/12 x = 10 x = 10 M  We need the (6 th and 7 th interval) / 2 M  We need the (6 th and 7 th interval) / 2 X 6 = 10 X 6 = 10 X 7 = 15 X 7 = 15 M = 10 + 15 M = 10 + 15 2 M = 12.5

21. Solution Mode is the value with the biggest frequency Mode is the value with the biggest frequency Mode = 15 Mode = 15 Range is the highest – lowest Range is the highest – lowest Range = 15-2 = 13 Range = 15-2 = 13 Another example (optional) Another example (optional)

22. Missing Data These questions are given to see if you UNDERSTAND what the statistics mean These questions are given to see if you UNDERSTAND what the statistics mean Tricks  x = SUM Tricks  x = SUM n Sum = x x n Sum = x x 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!

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

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

25. Missing Data Ex#3: 10,12,15,19,21 n=7, x=15, Median=15, Mode=0 R = 16 Ex#3: 10,12,15,19,21 n=7, x=15, Median=15, Mode=0 R = 16 Missing 2: A & B Missing 2: A & B Sum = n x x Sum = n x x 7 x 15 = 105 7 x 15 = 105 Sum (now) = 10 + 12 + 15 + 19 + 21 = 77 Sum (now) = 10 + 12 + 15 + 19 + 21 = 77 Thus A + B = 105 – 77 = 28 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! 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, Try A – B = 16 Thus, A + B = 28 (respecting sum rule) A + B = 28 (respecting sum rule) A – B = 16 (respecting range) A – B = 16 (respecting range) 2A = 44 2A = 44 A = 22 (missing) A = 22 (missing) B = 6 B = 6