Day 5 Agenda: DG2 --- 20 minutes THQ1 Due Tues, 1/16 --- no late quizzes accepted
Advanced Placement Statistics Chapter 2 Advanced Placement Statistics Chapter 2.1: Measures of Relative Standing and Density EQ: What is meant by standardized value and how is it calculated?
Locations for data values within a data set are stated in terms of percentiles or z-scores. Consider the following sample test scores for a stat class:
a) Create a split stem and leaf for this distribution Scores on AP Stat Test KEY: 7|8 = 78
b) Find the 5-number summary of this data. Min = 67 Max = 93 Median = 80 Q1 = 76 Q3 = 83.5
c). Jenny’s score is in red c) Jenny’s score is in red. How did she perform relative to her classmates? Jenny scored higher than 75% of the other students in her class.
Standardized Scores: If the mean and standard deviation of a distribution are known the z-score is: z = x - mean standard deviation
Find the z-score for Jenny’s test. How did Jenny perform relative to her class? Jenny’s score was 0.988 standard deviations above the class mean. What about Kevin? Kevin’s score was the class mean. What about Katie? Katie’s score was 1.32 standard deviations below the class mean.
Find the z-score for each person’s score on the stat test. (Let lists in your calculator do all of the work.) 79 81 80 77 73 83 74 93 78 80 75 67 73 77 83 86 90 79 85 83 89 84 82 77 72 What is a score of 77 relative to the class? A score of 77 is 0.49 standard deviations below the class mean. What is a score of 89 relative to the class? A score of 89 is 1.48 standard deviations above the class mean.
Interpreting z-scores: Make the statement “ __________ standard deviations above/below the __________ mean.” DO NOT USE THE NEGATIVE SIGN IN YOUR STATEMENT.
Percentiles Percentiles are based on how many values in the data set are equal to or below the observed value. Find the percentile rank of Jenny, Kevin, and Katie.
EQ: What is represented under a density curve? Density Curves --- overall pattern of a distribution
Assignment: p. 118 #1, 2, 3 p. 121 #5, 6, 7, 8 p. 128 #10, 12, 13 p. 131 #15, 16, 19