Warm – Up 1. Find the IQR and Variance of the following data set. Are there any outliers in the data set? How do you know? Grades: 86, 78, 97, 96, 89, 92, 54, 94 IQR = 13 Variance = 202.502 Outliers: xi > Q3 + 1.5·(IQR) or xi < Q1 - 1.5·(IQR) xi > 95 + 1.5(13) xi < 82 - 1.5(13) xi > 114.5 xi < 62.5 So, 54 is one.

Warm - Up 1. What does this graphical display tell you about the temperature of coffee placed in the various containers after 5 minutes? 2. Construct a Box Plot and Identify any Outliers

2. Construct a Box Plot and Identify any Outliers Xi > Q3 + 1.5∙(IQR) = Xi > 78 + 1.5(10) = 93 Xi < Q1 - 1.5∙(IQR) = Xi < 68 - 1.5(10) = 53 No Outliers Pulse (beats/min) 55 60 65 70 75 80 85 90

4 Complete Response All three parts essentially correct 3 Substantial Response Two parts essentially correct and one part partially correct 2 Developing Response Two parts essentially correct and one part incorrect OR One part essentially correct and one or two parts partially correct Three parts partially correct 1 Minimal Response One part essentially correct and two parts incorrect Two parts partially correct and one part incorrect

Warm – Up 1. Find the IQR and Variance of the following data set. Are there any outliers in the data set? How do you know? Grades: 86, 78, 97, 96, 89, 92, 54, 94 IQR = 13 Variance = 202.502 Outliers: xi > Q3 + 1.5·(IQR) or xi < Q1 - 1.5·(IQR) xi > 95 + 1.5(13) xi < 82 - 1.5(13) xi > 114.5 xi < 62.5 So, 54 is one. 2. What does Standard Deviation measure? Is this statistic Nonresistant or Robust? The Spread or Variation in relation to the mean among the data points in a distribution. Nonresistant.

CHAPTER 5 (continued)

More with Standard Dev. (Chapter 5 continued): When the standard deviation, s, equals zero then there is NO SPREAD (all the observations have the same value). Otherwise s > 0. As the observations become more spread out the standard deviation, s, gets much larger. EX.) Put the following in ascending order by their Standard Deviation (smallest ‘s’ to largest.) a.) 6, 9, 15, 18 b.) 0, 8, 16, 24 c.) 12, 12, 12, 12 c (s = 0), a, b

The formula for Standard Deviation has you Square the differences or Deviations….why? The Mean of each data set is 12. The deviations are as follows: a.) 6, 9, 15, 18 b.) 0, 8, 16, 24 c.) 12, 12, 12, 12 -6, -3, 3, 6 -12, -4, 4, 12 0, 0, 0, 0

What does this slide indicate? Standard Deviation of US Climate (1971 – 2000) (The darker the green is, the Higher the Standard Deviation) What does this slide indicate?

Cumulative Relative Frequency Histogram Med = 50%=0.5 Q1 = 25%=0.25 72 70.5 73.5 HEIGHTS IN INCHES OF A MEN BB TEAM

Mean or Median? Regardless of the shape of the distribution, the median is the point at which a histogram of the data would balance: n=192

HW: Page 95; 27,28,34-36

TIME PLOTS A Time Plot of a variable plots each Observation against the time at which it was measured. Time is ALWAYS the Horizontal Axis. EXAMPLE: 1999 2000 2001 2002 2003 2004 % of 5’s 8 12 12 15 16 21 You see an UPWARD TREND 5 10 15 20 25 Percent of 5’s 1999 2000 2001 2002 2003 2004 TIME IN YEARS

Construct a Histogram and a Boxplot for the following Data Construct a Histogram and a Boxplot for the following Data. Describe the distribution and find the Mean and Median. 12, 14, 11, 11, 13, 14, 18, 10, 12, 12, 15, 12, 17 Mean = 13.154 Median = 12 If the Mean is (roughly) equal to the Median then the distribution is symmetric. If the Mean is greater than the Median then the distribution is skewed right. If the Mean is less than the Median then the distribution is skewed left.