Elementary Statistics Chapter 2 PDF

CHAPTER 2 Elementary Statistics Copyright © 2010, 2007, 2004 Pearson Education, Inc. 2.1 - 1 2.1 - 2 2.1 - 3 Pulse Rates of Females and Males Original Data 2.1 - 4  Puls...

CHAPTER 2 Elementary Statistics Copyright © 2010, 2007, 2004 Pearson Education, Inc. 2.1 - 1 2.1 - 2 2.1 - 3 Pulse Rates of Females and Males Original Data 2.1 - 4  Pulse Rates of Females and Males Original Data 60-69 2.1 - 5 Frequency Distribution Pulse Rates of Females The frequency for a particular class is the number of original values that fall into that class. 2.1 - 6  Lower Class Limits are the smallest numbers that can actually belong to different classes Lower Class Limits Copyright © 2010, 2007, 2004 Pearson Education, Inc. 2.1 - 7  Upper Class Limits are the largest numbers that can actually belong to different classes Upper Class Limits 2.1 - 8  Class Boundaries are the numbers used to separate classes, but without the gaps created by class limits 59.5 69.5 79.5 Class 89.5 Boundaries 99.5 109.5 119.5 129.5 2.1 - 9  Class Midpoints are the values in the middle of the classes and can be found by adding the lower class limit to the upper class limit and dividing the sum by two 64.5 74.5 84.5 Class Midpoints 94.5 104.5 114.5 124.5 2.1 - 10  Class Width is the difference between two consecutive lower class limits or two consecutive lower class boundaries 10 10 Class 10 Width 10 10 10 2.1 - 11 2.1 - 12 10 2.1 - 13 Relative Frequency Distribution includes the same class limits as a frequency distribution, but the frequency of a class is replaced with a relative frequencies (a proportion) or a percentage frequency ( a percent) class frequency relative frequency = sum of all frequencies percentage class frequency =  100% frequency sum of all frequencies 2.1 - 14 Relative Frequency Distribution * Total Frequency = 40 * 12/40  100 = 30% 2.1 - 15 Cumulative Frequency Distribution Cumulative Frequencies 2.1 - 16 Frequency Tables 2.1 - 17  Other Information Midpoint: (lower limit + upper limit) / 2 Relative frequency: class frequency/total frequency Cumulative frequency: Number of values in that class or in lower. Class Midpoint Relative Cumulative f frequency Frequency (67+ 78)/2 3/30 67 - 78 3 72.5 0.10 3 79 - 90 5 84.5 0.17 8 91 - 102 8 96.5 0.27 16 103 -114 9 108.5 0.30 25 115 -126 5 120.5 0.17 30 18 30 2.1 - 18  Critical Thinking Interpreting Frequency Distributions In later chapters, there will be frequent reference to data with a normal distribution. One key characteristic of a normal distribution is that it has a “bell” shape.  The frequencies start low, then increase to one or two high frequencies, then decrease to a low frequency.  The distribution is approximately symmetric, with frequencies preceding the maximum being roughly a mirror image of those that follow the maximum. 2.1 - 19 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 2.1 - 20  Recap In this Section we have discussed  Important characteristics of data  Frequency distributions  Procedures for constructing frequency distributions  Relative frequency distributions  Cumulative frequency distributions 2.1 - 21