STATISTICS & PROBABILITY IN ELEMENTARY & MIDDLE SCHOOL. by RICK A. CAZZATO Hinsdale South...

STATISTICS & PROBABILITY IN ELEMENTARY & MIDDLE

SCHOOL.by

RICK A. CAZZATOHinsdale South High School

If you were to flip a coin 50 times, the outcome in one of the two columns.

Now, flip a coin 50 times and record the results.

Numb3s Handout

Randomization

Random Rectangle Handout

Tuesday, April 18, 2023

1. Look at the rectangle sheet and write down the average area of the rectangles on the sheet, you have 10 seconds to do this. Turn your paper over and write your answer on the back of the sheet.

2. Select ten of the rectangles, in your judgment, that are representative of the rectangles, write down the area for each ten and calculate the average. How does this compare to your guess?

3. Make a dot plot, 5 point summary, box and whiskers, of the classes guesses and subjective guesses.

4. Use the random digit table and select a SRS of size 10.

5. Compute the average of the your SRS and the classes.

6. How does this compare?7. Make a dot plot, 10 point

summary, box and whiskers, and 10 of the classes SRS.

Mean = 7.420Median = 6Stdev = 5.228Min = 1Max = 18Q1 = 4Q3 = 12

area0 2 4 6 8 10 12 14 16 18 20

Collection 1 Dot Plot

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area0 2 4 6 8 10 12 14 16 18 20

Collection 1 Histogram

One Variable Statistics

Pretend you are little kids sharing and the blocks are candy.

Determine how to share the candy in the group equally. For Group of 4’s: Group of 3’soldest gets 3 oldest gets 11Second oldest gets 6 middle gets 3Third oldest gets 10 youngest gets 10youngest gets 5

chips3 4 5 6 7 8 9 10 11

Groups of 4 Dot Plot

chips3 4 5 6 7 8 9 10 11

Groups of 4 Dot Plot

chips3 4 5 6 7 8 9 10 11

Groups of 4 Dot Plot

Count3 4 5 6 7 8 9 10 11 12

Candy Dot Plot

Count3 4 5 6 7 8 9 10 11 12

Candy Dot Plot

Count3 4 5 6 7 8 9 10 11 12

Candy Dot Plot

If we have six tests this semester, youwant an 80% average, with the grades{86,79,73,82,82,}, what does your nextgrade need to be to earn an 80%?

7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6

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Collection 1

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ID Candy ServingSize TotalCalories FatCalories TotalFat <new>

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1 Mr. Good Bar 49 280 160 18

2 Hershey Chocolate Bar 43 230 120 13

3 Hershey Chocolate Bar with Almonds 41 230 130 14

4 Almond Joy 36 180 90 10

5 Hershey Rolo 54 230 110 12

6 5th Avenue 57 280 110 12

7 Reese's Cup 45 240 130 14

8 Kit Kat 42 220 110 12

9 Nut Rageous 45 250 140 15

10 Peppermint Patty 42 170 35 4

11 Heath Bar 40 210 100 13

12 Twix 57 280 130 14

13 Snickers 59 280 120 14

14 Milky Way 61 280 100 11

15 3 Musketeers 60 260 70 8

16 Clark Bar 50 240 90 10

17 100 Grand 43 200 70 8

18 Baby Ruth 60 280 110 12

19 Nestle Milk Chocolate 41 220 110 13

20 Butterfinger 42 200 70 8

1 Mr. Good Bar 49 280 160 18

Collection 1

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ID Candy ServingSize TotalCalories FatCalories TotalFat <new>

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1 Mr. Good Bar 49 280 160 18

2 Hershey Chocolate Bar 43 230 120 13

3 Hershey Chocolate Bar with Almonds 41 230 130 14

4 Almond Joy 36 180 90 10

5 Hershey Rolo 54 230 110 12

6 5th Avenue 57 280 110 12

7 Reese's Cup 45 240 130 14

8 Kit Kat 42 220 110 12

9 Nut Rageous 45 250 140 15

10 Peppermint Patty 42 170 35 4

11 Heath Bar 40 210 100 13

12 Twix 57 280 130 14

13 Snickers 59 280 120 14

14 Milky Way 61 280 100 11

15 3 Musketeers 60 260 70 8

16 Clark Bar 50 240 90 10

17 100 Grand 43 200 70 8

18 Baby Ruth 60 280 110 12

19 Nestle Milk Chocolate 41 220 110 13

20 Butterfinger 42 200 70 8

1 Mr. Good Bar 49 280 160 18

Calculate the mean of the Total Fat in grams for each candy bar.

Mean

What do you notice?

Mean

What do you notice?

Mean

Mean

Mean

Line up according to the number of hours of sleep you had last night, round to the nearest ten minutes.How can we represent this data graphically?

How can we represent this data numerically?

The prices, in dollars, of nine homes in West Chicago are given below:79,000 135,000 170,000575,000 137,000 148,000153,000 79,000 110,000

The mean is $179222.22.The median is $137,000.The mode is $79,000.Which statistic is best? Why?

In a press release by the University of North Carolina’s Alumni Association in the 1980’s, they reported that the average starting salary for graduating geography majors was $300,000. What do you think about this statement?

State Names Activity Sheet

Letters of the States

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States Histogram

0 | 0 1 2 2 2 4 5 6 8 81 | 0 1 1 2 4 5 5 92 | 2 8 Key: 3 | 6 means 363 | 2 64 | 3 45 | 6 | 1

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States Box Plot

Two Variables

Name armspan height gender

Mr. C 188.5 181 m

Amy 167.3 169.5 f

Kim 166.2 168.3 f

Arsen 179.5 177.5 m

Muff 180 177 m

Maggie 164.7 166.6 f

Class Data

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Generation0 1 2 3 4 5 6 7 8 9

Tacks Scatter Plot

Extra Stuff

Laura earned the following grades during the year: 74, 78, 73, 74, 70, 68, 39, 74, 76, 74.In the class a 72 is a earns a C grade. Should Laura earn a C for the year? Explain your reasoning by writing complete sentence.

The Environmental Protection Agency (EPA) performs extensive tests on all new car models to determine their mileage ratings. The next screen represents the results of such tests on new car models. What can you tell me about these ratings?

26.3 31 26.9 27.1 34.9 26.8 20 27.2 32.1 26.722.7 27.3 31.2 26.6 22.9 26.5 23.2 27.4 27.5 23.630.5 26.5 27.6 23.9 30.2 26.4 27.7 27.7 30 24.226.2 27.9 26 27.9 25.9 28.2 28.3 25.7 25.6 25.128.5 29 25.5 24.8 28.6 29.4 25.3 24.4 28.8 29.726.3 26.8 22.5 26.4 30.5 26.6 26.1 28.2 28.4 29.331 21.8 27.3 23.1 27 27.6 27 28.7 29 25.727 27.2 30.7 27.4 27.1 27.8 25.9 25.6 26.7 24.5

27.1 30.3 26.7 27 23.9 30.1 28 25.2 24.8 29.529.9 26.9 22.9 23.8 29.8 24 26.8 25 28.1 26.9

20 22 24 26 28 30 32 34 36Mileage

EPA Mileage Ratings Dot PlotDOT PLOT

What can you tell me now?

EPA Mileage Ratings

20|021|822|5 7 9 923|1 2 6 8 9 924|0 2 4 5 8 825|0 1 2 3 5 6 6 7 7 9 926|0 1 2 3 3 4 4 5 5 6 6 7 7 7 8 8 8 9 9 927|0 0 0 0 1 1 1 2 2 3 3 4 4 5 6 6 7 7 8 9 928|0 1 2 2 3 4 5 6 7 829|0 0 3 4 5 7 8 930|0 1 2 3 5 5 731|0 0 232|133|34|9

What can you tell me now?

Stem & Leaf Plot

KEY263 means 26.3 miles

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EPA Mileage Ratings HistogramHistogram

What can you tell me now?

Write complete sentences for the following questions.

1. What are some advantages to each representation?

2. What are some disadvantages to each representation?

3. How would you create a stem & leaf plot?

4. How would you create a histogram?5. How are the stem & leaf plot and

histogram related?

EPA Mileage Ratings

20|021|822|5 7 9 923|1 2 6 8 9 924|0 2 4 5 8 825|0 1 2 3 5 6 6 7 7 9 926|0 1 2 3 3 4 4 5 5 6 6 7 7 7 8 8 8 9 9 927|0 0 0 0 1 1 1 2 2 3 3 4 4 5 6 6 7 7 8 9 928|0 1 2 2 3 4 5 6 7 829|0 0 3 4 5 7 8 930|0 1 2 3 5 5 731|0 0 232|133|34|9

Stem & Leaf Plot

KEY263 means 26.3 miles

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EPA Mileage Ratings Histogram

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items: 100

minimum value: 20.000first quartile: 25.625median: 27.000third quartile: 28.375maximum value: 34.900

mean value: 26.993midrange: 27.450

range: 14.900interquartile range: 2.750mean deviation: 1.801sample std dev (n): 2.406sample std dev (n-1): 2.418

Key concepts are• Categorical & quantitative

variables• Discrete or continuous variables• Representing data graphically• Symmetry, skewed left or right• Uniform distribution• Center, outliers, spread

(variability), gaps, clusters

GOAL to graphically and numerically represent data sets, determine advantages and disadvantages of these representations, and associated vocabulary.

Line up according to the number of minutes of sleep you had last night.

Comparative Stem and Leaf DiagramStudent Age

female male 7 1 9999 1 8888899999999999999991111000 2 000000011111111113322222 2 2222223333 4 2 445 2 6 2 88 0 3 3 3 7 3 8 3 4 4 4 4 7 4

From this comparative stem and leaf diagram, it is clear that the male ages are all more closely grouped then the females. Also the females had a number of outliers.

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Summary TableSpinning

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S1 = sum