statistics & probability in elementary & middle school. by rick a. cazzato hinsdale south...
TRANSCRIPT
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STATISTICS & PROBABILITY IN ELEMENTARY & MIDDLE
SCHOOL.by
RICK A. CAZZATOHinsdale South High School
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If you were to flip a coin 50 times, the outcome in one of the two columns.
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Now, flip a coin 50 times and record the results.
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Numb3s Handout
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Randomization
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Random Rectangle Handout
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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.
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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?
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3. Make a dot plot, 5 point summary, box and whiskers, of the classes guesses and subjective guesses.
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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.
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Mean = 7.420Median = 6Stdev = 5.228Min = 1Max = 18Q1 = 4Q3 = 12
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area0 2 4 6 8 10 12 14 16 18 20
Collection 1 Dot Plot
Co
un
t
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area0 2 4 6 8 10 12 14 16 18 20
Collection 1 Histogram
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One Variable Statistics
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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
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chips3 4 5 6 7 8 9 10 11
Groups of 4 Dot Plot
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chips3 4 5 6 7 8 9 10 11
Groups of 4 Dot Plot
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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
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Count3 4 5 6 7 8 9 10 11 12
Candy Dot Plot
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Count3 4 5 6 7 8 9 10 11 12
Candy Dot Plot
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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
XX X XX
17 6
2
2
X
2
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Collection 1
=
ID Candy ServingSize TotalCalories FatCalories TotalFat <new>
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
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
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Collection 1
=
ID Candy ServingSize TotalCalories FatCalories TotalFat <new>
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
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.
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Mean
What do you notice?
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Mean
What do you notice?
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Mean
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Mean
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Mean
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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?
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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?
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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?
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State Names Activity Sheet
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Letters of the States
0
10
20
30
40
50
60
70
A B C D E F G H I J K L M N O P Q R S T U V W X Y
Letter
Fre
qu
ency
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Co
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8
0 10 20 30 40 50 60 70 80Frequency
States Histogram
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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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Frequency
0 10 20 30 40 50 60 70
States Box Plot
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Two Variables
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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
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Class Data
160
165
170
175
180
185
190
160 165 170 175 180 185 190
Height
Arm
span
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Gro
up
C
0
20
40
60
80
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120
Generation0 1 2 3 4 5 6 7 8 9
Tacks Scatter Plot
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Extra Stuff
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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.
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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?
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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
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20 22 24 26 28 30 32 34 36Mileage
EPA Mileage Ratings Dot PlotDOT PLOT
What can you tell me now?
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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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5
10
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20
25
30
Co
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18 20 22 24 26 28 30 32 34 36 38Mileage
EPA Mileage Ratings HistogramHistogram
What can you tell me now?
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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?
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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
4
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20|0
21|8
22|5
799
23|1
2689
924
|024
588
25|0
1235
6677
9926
|012
3344
5566
7778
8899
927
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4456
6778
9928
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2345
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0345
789
30|0
1235
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|002
32|1
33|
34|9
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5
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Co
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18 20 22 24 26 28 30 32 34 36 38Mileage
EPA Mileage Ratings Histogram
20|0
21|8
22|5
799
23|1
2689
924
|024
588
25|0
1235
6677
9926
|012
3344
5566
7778
8899
927
|000
0111
2233
4456
6778
9928
|012
2345
678
29|0
0345
789
30|0
1235
5731
|002
32|1
33|
34|9
20|0
21|8
22|5
799
23|1
2689
924
|024
588
25|0
1235
6677
9926
|012
3344
5566
7778
8899
927
|000
0111
2233
4456
6778
9928
|012
2345
678
29|0
0345
789
30|0
1235
5731
|002
32|1
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34|9
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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
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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
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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.
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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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