Elementary Statistics Chapter 2 PDF

CHAPTER 2 Elementary Statistics Copyright © 2010, 2007, 2004 Pearson Education, Inc. 2.1 - 1 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 2.1 - 2 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 2.1 - 3 P...

CHAPTER 2 Elementary Statistics Copyright © 2010, 2007, 2004 Pearson Education, Inc. 2.1 - 1 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 2.1 - 2 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 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  Hours of Television Watched 20 Number of students 16 12 8 4 0 1-3 4-6 7-9 Hours 2.1 - 22  Key Concept We use a visual tool called a histogram to analyze the shape of the distribution of the data. 2.1 - 23  Histogram A graph consisting of bars of equal width drawn adjacent to each other (without gaps). The horizontal scale represents the classes of quantitative data values and the vertical scale represents the frequencies. The heights of the bars correspond to the frequency values. 2.1 - 24 2.1 - 25 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 2.1 - 26  Histogram Basically a graphic version of a frequency distribution. 2.1 - 27  Histogram The bars on the horizontal scale are labeled with one of the following: (1) Class boundaries (2) Class midpoints (3) Lower class limits (introduces a small error) Horizontal Scale for Histogram: Use class boundaries or class midpoints. Vertical Scale for Histogram: Use the class frequencies. 2.1 - 28  Frequency Histogram Class f Boundaries 67 – 78 3 66.5 - 78.5 79 - 90 5 78.5 - 90.5 91 - 102 8 90.5 - 102.5 Time on Phone 9 9 8 103 -114 9 102.5 -114.5 8 7 115 -126 5 114.5 -126.5 6 5 5 5 f 4 3 3 2 1 0 66.5 78.5 90.5 102.5 114.5 126.5 minutes 29 2.1 - 29 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 2.1 - 30 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 2.1 - 31 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 2.1 - 32 Copyright © 2010, 2007, 2004 Pearson Education, Inc. 2.1 - 33  Relative Frequency Histogram Has the same shape and horizontal scale as a histogram, but the vertical scale is marked with relative frequencies instead of actual frequencies 2.1 - 34  Critical Thinking Interpreting Histograms Objective is not simply to construct a histogram, but rather to understand something about the data. When graphed, a normal distribution has a “bell” shape. Characteristic of the bell shape are (1) The frequencies increase to a maximum, and then decrease, and (2) symmetry, with the left half of the graph roughly a mirror image of the right half. The histogram on the next slide illustrates this. 2.1 - 35 2.1 - 36  Recap In this Section we have discussed  Histograms  Relative Frequency Histograms 2.1 - 37  Key Concept This section discusses other types of statistical graphs. Our objective is to identify a suitable graph for representing the data set. The graph should be effective in revealing the important characteristics of the data. 2.1 - 38 2.1 - 39  Frequency Polygon Uses line segments connected to points directly above class midpoint values 2.1 - 40  Frequency Polygon Class f Time on Phone 67 - 78 3 9 9 8 79 - 90 5 8 7 91 - 102 8 6 f 5 5 5 103 -114 9 4 3 3 115 -126 5 2 1 0 72.5 84.5 96.5 108.5 120.5 minutes Mark the midpoint at the top of each bar. Connect consecutive midpoints. Extend the frequency polygon to the axis. 41 2.1 - 41  Relative Frequency Polygon Uses relative frequencies (proportions or percentages) for the vertical scale. 2.1 - 42  Ogive A line graph that depicts cumulative frequencies 2.1 - 43  Ogive An ogive reports the number of values in the data set that are less than or equal to the given value, x. Cumulative Frequency Minutes on Phone 30 30 25 20 16 10 8 3 0 0 66.5 78.5 90.5 102.5 114.5 126.5 minutes 44 2.1 - 44