Warm-Up: Create a Boxplot.

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2 Warm-Up: Create a Boxplot. 2

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5 Warm - UP Find the mean. 3. Find the standard deviation for the set { 54, 59, 35, 41, 22}

6 Warm - UP

7 How many hours do you spend watching TV or surfing the net each day ( none educational)?

8 Boxplot The number of hysterectomies performed by a sample of 15 male doctors are arranged in order. 20,25,25,27,28,31,33, 34, 36,37,44, 50,59, 85, 86

9 Minimum Lower Upper Quartile Quartile Median Maximum Box and Whisker Plots

10 Student will be able to arrange data from a given data set using the boxplot.

11 Connection A box-and-whisker plot can be useful for handling many data values. They allow people to explore data and to draw informal conclusions when two or more variables are present. It shows only certain statistics rather than all the data. Box and whisker plots consists of the median, the quartiles, and the smallest and greatest values in the distribution.

12 Vocabulary Interquartile Range abbreviated IQR, is defined as the distance between the first and third quartiles. The five-number summary of a data set consists of the smallest observation, the first quartile, the median, the third quartile, and the largest observation, written in order from smallest to largest in the symbols, the five summary is Minimum Q 1 M Q 3 Maximum Modified Boxplot Plots outliers as isolated points. The first, highest none outlier point is used for the maximum and minimum. Outlier Data point that falls more than 1.5 X IQR below Q 1 or above Q 3. Quartiles marks out the middle of half of the data. The first quartile is onequarter of the way up the list. The third quartile is three-quarters of the way up the list. The second quartile is the median, which is larger than 50% of the observations. The first quartile is larger than 25% of the list. The third quartile is larger than 75% of the list.

13 Calculating Quartiles 1. Arrange the observations in increasing order and locate the median of M in the ordered list of observations. 2. The first Q1 is the median of the observations whose position in the ordered list is the left of the location of the overall median. 3. The third quartile Q3 is the median of the observation whose position in the ordered list is to the right of the location of the overall median.

14 How to make a Box and Whisker Plot 1. Put your set of date in increasing numerical order (if it isn t already). Example: 100, 27, 34, 54, 59, 18, 52, 61, 78, 68, 82, 87, 85, 93, 91. Should now look like this 18, 27, 34, 52, 54, 59, 61, 68, 78, 82, 85, 87, 91, 93, 100.

15 Step 2 - Median 2. Find the median of your set of data *Remember the median is the value exactly in the middle of an ordered set of numbers* 18, 27, 34, 52, 54, 59, 61, 68, 78, 82, 85, 87, 91, 93, 100. Q: What would you do it you had an even set of numbers?

16 Step 3 Lower Quartile 3. Next, we consider only the values to the left of the median 18, 27, 34, 52, 54, 59, 61, 68, 78, 82, 85, 87, 91, 93, 100. We find the median of those numbers 18, 27, 34, 52, 54, 59, 61 Q: This number is call the lower quartile. Can you guess why?

17 Step 4 Upper Quartile 4. Next, we consider only the values to the right of the median 18, 27, 34, 52, 54, 59, 61, 68, 78, 82, 85, 87, 91, 93, 100. We find the median of those numbers 78, 82, 85, 87, 91, 93, 100. Q: This number is call the upper quartile. Can you guess why?

18 Step 5 Highest/Lowest Values 5. Now indicate your lowest and highest values 18, 27, 34, 52, 54, 59, 61, 68, 78, 82, 85, 87, 91, 93, 100.

19 Step 6 - Drawing 6. Now we are ready to begin to draw our graph. 18, 27, 34, 52, 54, 59, 61, 68, 78, 82, 85, 87, 91, 93, 100. Plot the lowest value, lower quartile, median, upper quartile, and the highest value on a number line.

20 Put a line through the Lower Quartile, Median, and Upper Quartile. Then Put a box around those lines

21 Lastly draw a line from your extreme values to the box There is your Box and Whisker Plot

22 Group Practice

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24 Time for a challenge activity 1/interpret-box-and-whisker-plots

25 Stem-Leaf Plot

26 Background Individuals are objects described by a set of data. Individuals may be people, but they may also be animals or things. A variable is an characteristic of an individual. A variable can be different values for different individuals. The distribution of a variable tells us what values the variables takes and how often it takes the values. Skewed to the right a distribution is skewed to the right if the right side of the historgram (containing the upper half of the observations) extends much farther out than the left side ( containing the lower half of the observations) Skewed to the left - A distribution is skewed to the left if the left side of the histogram extends farther out than the right side Symmetric A distribution is symmetric if the right and left sides of the histogram are approximately mirror images of each other. Copyright 2000 by Monica Yuskaitis

27 Skewed Histograms

28 Skewed Historgrams/Distrubitions

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35 Homework

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37 Warm-UP 37

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39 Rubric: Problem Completion - 5 points Presentation - 5 points Data set 3-Minute Presentations Categories for grouping data ( Interval or Range) Range of data set. Width The difference between the cutpoints of a class. Height of Bars/ Frequency 39

40 The Dot Plot What is it? How to Draw it Bet you ve never seen a graph like this one before...

41 What is a Dot Plot? A dot plot - A dot plot is a graph that shows the distribution of a quantitative variable above a number line with small periods, dots, circles or x s. It plots a quantitative variable against a quantitative variable. Axes on a dot plot.- A dot plot only has an x- axis. The y-axis is never drawn Advantage of a dot plot - Moderate amounts of quantitative data can be quickly visualized 41

42 What is a Dot Plot? 2 Variables on a dot plot: x-axis variable is quantitative and identified y-axis variable is implied since the y-axis is never drawn. y-axis variable is the count and so is normally discrete quantitative 42

43 Making a Dot Plot I want to know more about my students who take Intro Stats so I ve decided to take a survey and make a dot plot of the results I d like to find out about the pets they have in their household. The question then becomes: How many pets are in your household? 43

44 Making a Dot Plot from Live Data Frequency Frequency 0 pets 9 pets 1 pet 10 pets 2 pets 11 pets 3 pets 12 pets 4 pets 13 pets 5 pets 14 pets 6 pets 15 pets 7 pets 16 pets 8 pets 17 pets 44

45 Dot Plot Example Number of Pets Per Household for Ms. H's Intro Stat Classes Source: In Class Survey x-axis: # of Pets 45

46 Freq Table Example 4 Classes Combined Fre- Relative Class quency Freq 0 pets % 1 pet % 2 pets % 3 pets 8 6.0% 4 pets % 5 pets 7 5.2% 6 pets 2 1.5% 7 pets 3 2.2% 8 pets 2 1.5% 9 pets 1 0.7% 10 pets 1 0.7% 11 pets 3 2.2% 12 pets 0 0.0% 13 pets 1 0.7% 14 pets 0 0.0% 15 pets 0 0.0% 16 pets 0 0.0% 17 pets 0 0.0% 18 pets 0 0.0% 19 pets 0 0.0% 20 pets 0 0.0% 21 pets 0 0.0% 22 pets 0 0.0% 23 pets 0 0.0% 24 pets 0 0.0% 25 pets 0 0.0% 26 pets 0 0.0% % % % % Mean = 2.52 pets Median = 2 pets Mode = 0 pets (37x) Range = 30 pets Spread = 0-30 pets n = 134 students Totals 31 classes % 46

47 Dot Plot Example 4 Classes Combined. : : Number of Pets Per Household :. for Ms. H's Intro Stat Classes : : Oct 6, 2010 : :. : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :. : : : : : : : : : : : :.. : : : : : : : : :.. : Source: In Class Survey x-axis: # of Pets 47

48 Dot Plot: Statistical Vocabulary Background Spread (also called Variability) Range The spread of data in statistics is the smallest value in a data set and the largest value It is always expressed as 2 numbers Prefer to write smallest then largest number Units are important The range of data in statistics is the difference between the smallest value and the largest value Take the spread and subtract the two numbers: large small Units are important 48

49 Dot Plot: Statistical Vocabulary Background One Measure of Center Mode One measure of the center of a data distribution is the median, the place where the data tends to be ½ above and ½ below. Units are important The mode of data is a place or places with the largest number of data with the same value. Units are important. 49

50 Shape Dot Plot: How to Describe It The shape of a data distribution possibilities: 1) Symmetry Symmetric Also Fairly Symmetrical Skewed Left (negatively skewed) Skewed Right (positively skewed) 2) Peaks Single Peaked (unimodal) Double Peaked (bimodal) Multi Peaked (multimodal) NOTE: Data have modes, dot plots have peaks 50

51 Student Scores in Anderson s Cr Writing Name Gender 3rd Per Grade ID Test #10 Teacher No % 1 Benson, Paul M Kling Bishop, Sally F Smith Chan, Alex M Yale Chaney, Brenda F Fernando Darosa, Rick M Iijima Dovsten, Stan M Browne Dring, Pamela F Nikola Gomez, Tom M Lunceford Hart, Ron M Tyler Ho, DJ M Cedric Hughes, Kim F Dorman Kennedy, Fred M Ho Khangura, Sam M Horvath Lace, Bob M Kwok Lamar, Candy F Falck Lunda, Alice F Edwards Nester, Lucy F Ho Pomodor, Gorde M Horvath Prado, Cindy F Kang Rice, Dale M Duerr

52 Student Scores in Anderson s Cr Writing Anderson's English Class Test 101 Scores : :. :.... : Source: Teacher Records x-axis: Score in pts. 52

53 % of Population Over 65 1 Alabama Montana 13 2 Alaska 5 27 Nebraska 14 3 Arizona Nevada 11 4 Arkansas N Hampshire 12 5 California N Jersey 14 6 Colorado N Mexico 11 7 Connecticut N York 13 8 Delaware N Carolina 13 9 Florida N Dakota Georgia Ohio Hawaii Oklahoma Idaho Oregon Illinois Penn Indiana R Island Iowa S Carolina Kansas S Dakota Kentucky Tennessee Louisiana Texas Maine Utah 9 20 Maryland Vermont Mass Virginia Michigan Washington Minnesota W Virginia Mississippi Wisconsin Missouri Wyoming 11 53

54 Population over 65 Data Sorted by % 1 Alaska 5 26 Indiana 13 2 Utah 9 27 Kentucky 13 3 Colorado Alabama 13 4 Georgia Montana 13 5 Texas Arizona 13 6 N Mexico Wisconsin 13 7 California N York 13 8 Virginia Ohio 13 9 Wyoming Oklahoma Maryland Oregon Idaho Kansas Louisiana N Jersey Nevada Maine Washington Missouri N Hampshire Nebraska S Carolina Mass Vermont Connecticut Mississippi S Dakota Michigan Arkansas Minnesota N Dakota Illinois Iowa N Carolina W Virginia Tennessee R Island Delaware Penn Hawaii Florida 19 54

55 Make Dot Plot of State Population Data Percent of Population over 65 years of Age in the 50 States. : : : :. : : : : : :. : : : : :.. : : : : : : : Source: Statistical Abstract of the US x-axis: Number in % to nearest integer 55

56 Dot Plot: How to Describe It More on Shape Symmetric When the left & right sides of a distribution are mirror images of one another Fairly Symmetric When the left and right sides of a distribution are almost mirror images of one another, but there are small exceptions. Skewed Left (negatively skewed) If a distribution extends much farther out to the left. The direction of skewness is on the side of the longer tail, in this case LEFT. Skewed Right (positively skewed) If a distribution extends much farther out to the right. The direction of skewness is on the side of the longer tail, in this case RIGHT. 56

57 Dot Plot: What it Looks Like Shape: Symmetry Symmetric 57

58 Dot Plot: What it Looks Like More on Shape: Non Symmetric Skewed Left (negatively skewed) tail Left Skew Skewed Right (positively skewed) Right Skew tail 58

59 Goals by US Women s Soccer Number of Goals Scored by US Women's Soccer Team in 34 games in Source: US Soccer Assn. 59

60 Goals by US Women s Soccer Ordered Ascending

61 Dot Plot of Goals by US Women s Soccer Goals per Game by US Women's Soccer Team in 2004 : : : :. : : : : :. : : : : : : Source: US Women's Soccer Assn x-axis: # of goals per game 61

62 Living in Poverty East of the Mississippi Percent of State Residents Living in Poverty East of Mississippi River, 1999 Source: Stat Abs of US Alabama 13 Maryland 6 Penn 8 Connecticut 6 Mass 7 Rhode Is 9 Delaware 7 Michigan 7 S Caroliina 11 Florida 9 Mississippi 16 Tennessee 10 Georgia 10 New Hamp 4 Vermont 6 Illinois 8 New Jersey 6 Virginia 7 Indiana 7 NY 12 W Virginia 14 Kentucky 13 N Carolina 9 Wisconsin 6 Maine 8 Ohio 8 62

63 Living in Poverty East of the Mississippi Ordered Ascending New Hamp 4 Ohio 8 Wisconsin 6 Penn 8 Maryland 6 Rhode Is 9 Connecticu 6 Florida 9 New Jersey 6 N Carolina 9 Vermont 6 Georgia 10 Delaware 7 Tennessee 10 Indiana 7 S Caroliina 11 Mass 7 NY 12 Virginia 7 Alabama 13 Michigan 7 Kentucky 13 Illinois 8 W Virginia 14 Maine 8 Mississippi 16 63

64 Living in Poverty East of the Mississippi % of State Residents Living in Poverty East of.. the Mississippi River in 1999 : : :.. : : : : :.. : Source: Statistical Abstract of the US x-axis: Values to the nearest % 64

65 Dot Plot: Mean & Median Essentials Skew on a dot plot in relation to mean and median You ve drawn the line that connects the dot plot points on the top of the distribution. The line clearly shows right or left skew. If you have right skew, the mean will be to the right of (greater than) the median, as the mean follows the tail of the distribution. median mean Right Skew tail 65

66 Dot Plot: Mean & Median Essentials Skew on a dot plot in relation to mean and median If you have left skew, the mean will be to the left of (less than) the median, as the mean follows the tail of the distribution. mean median tail Left Skew 66

67 Dot Plot: Describing Peaks Peaks Unimodal Unimodal Bimodal Bimodal Multimodal (3 or more peaks) Trimodal or Multimodal 67

68 TI83 and Sort Ascending How to Sort Data in Ascending Order Enter all values in a list at STAT EDIT Exit to Home Screen using 2 nd MODE Hit STAT key. Go to #2 SORT A(. Hit ENTER Type 2 nd 1 (if the data is in List 1). Hit Enter Done appears Check your data in List 1. It should be sorted. Use your eyes to find the range & spread from the sorted list. 68

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70 Dot Plot: TI Essentials Finding Mean and Median Enter your data as a list in STAT EDIT Exit to home screen 2 nd Mode Go to 2 nd STAT. Right Arrow to MATH #3 is Mean; hit Enter; type 2 nd and list #; Enter #4 is Median; hit Enter; type 2 nd and list #; Enter Calculator does not give Mode. You need your eyes for that 70

71 Guided Practice 71

72 Glucose Blood Levels Glucose Blood Levels for Adult Women

73 Glucose Blood Levels GLUCOSE BLOOD LEVELS in mg/ml for 40 Women at Sutter Health in March 2009 : : :... : :.. :. :.. : : : :. : : Source: Sutter Health Clinic x-axis: glucose level in mg/ml 73

74 WBNA EAST Free Throws Data in Ascending Order Women's National Basketball Assn Free Throw Percentages for 1998 from WNBA

75 WBNA Free Throws Dot Plot WNBA EASTERN CONFERENCE FREE THROW PERCENTAGES :. :. :... :... :.. :. : : :.. : :. :... :. :. : Source: WNBA x-axis: %age of converted free throws per game 75

76 Dot Plot: How to Describe It Unusual Features. Possibilities include-- Potential Outliers: any data value that falls out of the pattern of the rest of the distribution. A potential outlier will lie at either extreme of the data when it is written in order. (We will learn how to calculate actual outliers later. For now, we will call these points potential outliers) Clusters: isolated groups of values. Clusters begin when frequency >1 and end before frequency returns to 1 or zero. Gaps: large spaces between values. Write gap values from beginning empty space to end empty space. A gap of one number is NOT a gap. 76

77 Fuel Consumption Data Fuel Consumption for 2009 Passenger Fords

78 Fuel Consumption Dot Plot Fuel Consumption for 2009 Passenger Fords. : :.. : : :... : :.. : :. :.. :. : : : Source: Consumer Reports x-axis: miles per gallon 78

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80 Saying

81 Warm-Up: Create a boxplot for the given data set.

82 Warm-up , 132, 136, 142, 145, 146, 149, 150, 151, 155, 158, 158, 161, 161, 165,165, 167, 170, 170, 172, 173, 173, 175, 175, 178,178,182, 182, 185, 187, 187, 188, 191, 209, 214, 218,

83 Classes - Categories for grouping data Frequency Distribution A listing of all classes and their frequencies Frequency ( or count) The number of observations that fall into a particular class is called the frequency (or count) of that class. Relative Frequency The percentage of a class, expressed as a decimal is called the relative frequency of the class. Lower Cutpoint The smallest value that go in a class. Upper Cutpoint Highest value that can go in a class Midpoint the middle of a class, found by averaging its cutpoints. Width The difference between the cutpoints of a class. Mark The Mark of a class is the average of a class is the average of its lower and upper limits.

84 Background Frequency histogram A graph that displays the classes on the horizontal axis and the frequencies of the classes on the vertical axis. The frequency of each class is represented by a vertical bar whose height is equal to the frequency. Relative Frequency histogram A graph that displays the classes on the horizontal axis and relative frequencies of the classes on the vertical axis. The relative frequency of each class is represented by a vertical bar whose height is equal to the relative frequency of the class.

85 Days to - Maturity

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87 Data Set: 32, 35, 39, 41, 41, 43, 43, 42, 40, 40, 43,45,46,47,48,46, 49,49, 51, 51

88 Data Set: 32, 35, 39, 41, 41, 43, 43, 42, 40, 40, 43,45,46,47,48,46, 49,49, 51,

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100 The following is a list of scores for Mr. Scott s math class. Use a histogram to represent the data. Use 10 units to categorize the data. 40, 41,42,54, 63, 66, 61, 69, 71,71,71, 75,78,78, 90,99,95,95,95,98,92, 92, 100,100,100

101 The following is a list of scores for Mr. Scott s math class. Use a histogram to represent the data. Use 10 units to categorize the data. 40, 41,42,54, 63, 66, 61, 69, 71,71,71, 75,78,78, 90,99,95,95,95,98,92, 92, 100,100,100

102 Guided Practice

103 Student Practice

104 Objective

105 Connections

106 Intro and background

107 Content

108 Guided Practice

109 Individual Practice

110 Guided Practice

111 Summary

112 Homework

113 B A D F G E C

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