Statistics Math 314 Game Plan Introduction n Presentation

Statistics Math 314

Game Plan Introduction n Presentation n Line graph n Pictograph n Bar graph n Histogram n Raw Stats n Frequency Stats n Missing Values n

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

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

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 n

Line Graph The Title of Your Graph Value Time

Pie or Circle Type n You need to add o your data Bass n Data Type # Bass 6 Salmon 12 Perch Total # % Angle 6 6/20 x 30 x 3. 6= 100% =30% 108° 12 12/20 x 60 x 3. 6 = 100% =60% 216° 2 2/20 x 10 x 3. 6= 100% =10% 36° 20 100 360°

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

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

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

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

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

Histogram n A bar graph is where the bars touch n Usually interested in intervals of numbers n Example: Given the data below, draw a histogram with an intervals of 50 n (3, 8, 9, 22, 46, 47, 80, 85, 87, 99) n We are thankful that they are in order; otherwise, put them in order!

Histogram Interval Tally f (frequency) [0, 50[ 6 [50, 100 ] 4 50 100

Raw Statistics (mean, median, mode & Range) Download / review slides on this topic n Analysis n Rule #1: Put them in order 1 st n Example: Calculate the mean, mode, median and range of the following… n (2, 7, 9, 12, 15) n Notice that they are in order! n

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

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

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

Solution x = 120/12 n x = 10 n M We need the (6 th and 7 th interval) / 2 n X 6 = 10 n X 7 = 15 n M = 10 + 15 2 M = 12. 5 n

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

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

Missing Data n n n n n Example #1: Given the following distributions, determine the missing value(s) 16, 23, 34, 15 n = 5 x = 32 Order 1 st! 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)

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

Missing Data n n n n Ex#3: 10, 12, 15, 19, 21 n=7, x=15, Median=15, Mode=0 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) 2 A = 44 A = 22 (missing) B=6