Unit 3 - Data. Grab a new packet from the chrome book cart. Unit 3 Day 1 PLUS Box and Whisker Plots.notebook September 28, /28 9/29 9/30?

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1 Unit 3 - Data Grab a new packet from the chrome book cart 9/28 9/29 9/30? 10/3 10/4 10/5 10/6 10/7-10/10 10/11 10/12 10/13 Practice ACT #1

2 Lesson 1: Box and Whisker Plots I can find the 5 number summary and use it to create a box and whisker plot by hand and by using a calculator Vocabulary Mean: Median: Mode: Range: IQR: 5 # summary:

3 Box and Whisker Plots How can we describe a box plot?

4 Let's collect some data: [1] Find your pulse rate and count for 30 seconds then MULTIPLY by 2. Plug into the calculator and find the mean, median, mode and 5 # summary mean: mode: range: 5 # summary: IQR

5 How are you doing?? Assignment: pg #1ab, 2-6, 8, 9b I can find the 5 number summary and use it to create a box and whisker plot by hand and by using a calculator

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7 Lesson Goals - 2 Days I can: Find Mean, Median, and Mode by hand and using the calculator. Find the 5 # Summary and use it to create a box and whisker plot by hand and by calculator Create data sets given information. Find Standard Deviation on a calculator and by hand.

8 Measures of Center: mean, median, mode Box Plots: 5 number summary,,,, Standard Deviation: {5, 3, 6, 9, 5, 20, 10, 7} Range: IQR: Outlier: 1.5x beyond Q1 or Q3 {3, 5, 5, 6, 7, 9, 10, 20} Cutoffs: and

9 Making up data sets Create a set of 3 numbers; range = 12; max = 20,, Create a set of 5; mean = 15; median = 14; mode = 20,,,, Create a set of 6; mean = 22 ; max = 25; mode = 20,,,,, Mastery Work: pg # 1ab, 2-6, 8, 9b, 10-12

10 Key pg [1] 29.2, 28, , 17.95, 17.4 [2] 7, 14, 15 (sum 36; 14 in middle) [3] 1.25, 2.5, 3.25, 4, 4.75 [4] B [5] D [8] 25, 51, 58, 65, 72; mean: 56.54; 98 [9b] range = 47; IQR = 14 [10] 9, 10, 11, 12, 13, 14, 15 (no repeat; sum 84) [11] 62, 63, 64, 65, 70, 70, 70 (many OK) [12] 33, 50, 53, 70, 72, 83, 92; pink may be different Warm Up: How do you... put data in Calculator? clear data? Find statistics? which symbol means mean? 5 number summary? standard deviation? What # make up a 5 number summary?

11 Lesson Goals - 2 Days I can: Find Mean, Median, and Mode by hand and using the calculator. Find the 5 # Summary and use it to create a box and whisker plot by hand and by calculator Create data sets given information. Find Standard Deviation on a calculator and by hand. Find 5 # summary; check for outlier; S x Adrian Peterson statistics for total yards per regular season game in the 2012 season {100, 180, 122, 103, 129, 159, 127, 193, 176, 138, 300, 170, 212, 110, 201}

12 Erase mean average distance spread Standard Deviation Sum (Add them all up) individual data value mean number of data values in the set 1. Find the standard deviation of the data set { 2, 4, 7, 8, 12, 15 } (Find the mean) (Deviations) 2 8 = = = = = =

13 Standard deviation is larger when the data is spread from the mean. Standard deviation is smaller when. Here are 4 volleyball teams with a plot of each players height in inches. Rank from smallest to biggest standard deviation. mean = 65.7 S x = 3.39 mean = 66 S x = 4.69 mean = 66 mean = 66 S x = 4.35 S x = 4.07

14 Which has the larger standard deviation? Mastery Work: pg # 2acd, 3-6, 9ab, 11, 13

15 Key pg [1] 47; -6, 8, 1, -3; 6.06 [2] 63.4; 11.24; minutes [3] 9, 10, 14, 17, 21; 12 & 7; cm [4] 18, 22, 28, 30, 35; 17 & 8 ; g [5] 72, 78, 84, 84, 85, 90, 95 [9] skewed left symmetric skewed has greater S x since farther apart [10] 47.1, 45.9, 47.9, 47.4, 45.1, 46, 45.3 S x = 1.08; 47.9 cm; 47.4 cm; 45.1 cm [11] 1st lowest and 6th largest [12] Juneau; 40.5 and , 30, 41, 51, & 21 NYC: and , 39, 54, 68.5, & 29.5 smaller spread in Juneau

16 Warm Up I can: Create and interpret a frequency table Create and interpret a histogram Calculate and interpret percentile rank

17 Histogram: a graph that shows the frequency of data values in the data set. 1) Bin widths should all be the same 2) The smaller the interval, the more you know about the specific numbers in the data set. 3) Boundary values always fall to the right. Heights of Plants in a Garden # of plants What values are in each bin??? Height (cm) Shape/Skew

18 1. Mound Shape Shape of Histograms What does a histogram with this shape mean about the data? = there are an amount of data pieces on the left and right of the with the same deviations from the mean. 2. Rectangular Shaped What does a histogram with this shape mean about the data?

19 3. Skewed Left What does a histogram with this shape mean about the data? erase the mean is than the median dropped lower Why?? 4. Skewed Right What does a histogram with this shape mean about the data? erase the mean is higher than the median Why??

20 The Percentile Rank of a data value gives the percentage of data values that are the given value. ex) Ellen scored in the 85th Percentile on her standardized test. What does this mean? How tall are you compared to your peers? Stretch break!! Line up from shortest to tallest. Gentleman 1 side and ladies other. Bring your calculator.

21 Find your percentile rank. Let's find out Mrs. W's together! Number in line: That means she was taller than people. What percentage of the ladies is that? Now do it for Follow up questions! Who was at the 25th percentile? What number would that be on a box plot? Who was at the 3rd quartile, Q 3? What percentile is that? Who was the median?

22 These data are the shoe sizes of 14 students. { 6, 7, 7, 7.5, 9, 9, 9.5, 10, 11, 11.5, 11.5, 12, 12, 13} a) Find the percentile rank of size 11.5 shoes. b) Find the percentile rank of size 9 shoe. c) What shoe size is in the 57 th percentile? d) What shoe size is in the 10 th percentile? 64 th percentile 29 th percentile size 11 size 7 Finding percentile rank from a histogram. 1) What is the percentile rank of a 75 foot tree? 2) In which interval is the 40th percentile?

23 Mastery Work: pages # 1ab; 4bc; 5ac (describe only); 8; 10 & Histogram & Percentile Rank WS (on google classroom - do work in note book.) Describe means write about without doing! Key [1] 2; 9; any that work [3] 5; 25%; 95% [2] 10; 15; 20; 25; iii not to 240 [4] more data in middle; mean = 2(26) + 3(56) etc / 1000 and between [5] More data to left [8] Better than 88%; = or lower to 12% Better than 95%; = or lower to 5% 99%; 10% [9] between mph; mph; location and safety

24 [6] dice sum roll grades on tests with most higher hard test with more low scores. Single die roll [10] 118; mph; 55 to 60 mph Warm Up You have the 3rd biggest foot in the room. What is your percentile rank? You have the 13th biggest foot. Rank? Your foot is in the 78 th Percentile. How many feet are smaller than yours?

25 Do in your note book. Real world use of normal distribution

26 Normal Distribution Curves I can: *Sketch a Normal Distribution Curve with the mean and standard deviations in the proper positions *Use the Normal curve to find percentile rankings *Use the Normal curve to find intervals for percentages of the distribution *Understand how the works and its relationship to standard deviation Rule (Empirical Rule): Normal Distributions with mean μ, SD σ *68% of observations fall within ±1σ of μ *95% of observations fall within ±2σ of μ *99.7% of observations fall within ±3σ of μ

27 Young women age 18 to 24 have an approximately normal distribution with mean height = 64 inches and a standard deviation = 3 inches. Sketch a Normal curve that shows the mean and ±3 standard deviations correctly located. 68% of the data fall between what numbers? 95%? 99.7%? What percentage of the data fall below 67 inches? above 61 inches? What percentage of the data fall between 58 and 67 inches? If a young woman is 70 inches tall, what percentile would she be at? Mastery Work: pg. 109 # 3 and 5 Normal Distribution WS (on google classroom - do in notebook with 1/2 sheet of graphs.)

28 Key [1] Plot B; Largest Spread [2] 30 for A and 25 for B B has largest spread [3] 553.6; 167; no mode 5, 167, 460, 645, 2019 (5 number) Skewed Right IQR: 478 Outliers 1822; 2019 [4] Sx = 3.1 IQR = Sx = 2.2 IQR = 5 [5] mean = Sx = Antarctica's High Outlier

29 % in 74 in 16% %

30 16% 99.7% 2.5%

31 hrs up to 49 hrs

32 68% 16% 16%