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# Statistics Notes week 2 Statistics 2228

ECU

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## Popular in Elementary Statistical Methods (Dr. Teresa Obuowska)

## Popular in Mathematics (M)

This 7 page Class Notes was uploaded by Rebecca Weidner on Monday February 1, 2016. The Class Notes belongs to Statistics 2228 at East Carolina University taught by Dr. W. Teresa Obuchowska in Spring 2016. Since its upload, it has received 79 views. For similar materials see Elementary Statistical Methods (Dr. Teresa Obuowska) in Mathematics (M) at East Carolina University.

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Date Created: 02/01/16

Chapter 2 Continued: Example: An analyst of trail derailments showed that (A) 23 derailments are caused by bad tracks. (B) 9 are caused by faulty equipment (C)12 are caused by human error (D)6 are caused by other causes Construct the frequency table: Category Frequency Relative frequency A. Derailment 23 .46 (46%) B. Faulty Eq. 9 .18 (18%) C. Human Err. 12 .24 (24%) D. Other 6 .06 (6%) Sum 50 1 (100%) How to construct the bar graph: 25 20 15 Frequesncy 10 5 0 derailment faulty equipment human erroother Categories How to construct the relative frequency bar graph: 0.45 0.4 0.35 0.3 0.25 0.2 0.15 RELATIVE Frequency 0.1 0.05 0 Categories How to construct a pie chart: 1. Always use a 2-dimentional circle for pie charts and NO other shape. - an ellpse will cause the sectors to be distorted depending on their placement. 2. Take each relative frequency for the different categories and then multiply them by 360 to get the proper angle for that sector of the circle. Relative frequencies Angle measure .46 46% .46 * 360 = 165.6 degrees .18 18% .18 * 360 = 64.8 degrees .24 24%4 .24 * 360 = 86.4 degrees .06 6% .06 * 360 = 21.6 degrees = 1 100% All should = 360 degrees 3. Draw a circle and measure out the sectors according to the table. derailment faulty eq. human error other Graphs for Qualitative Bivariate Data 1. Two side-by-side pie charts. 2. Two side-by-side bar charts, in which bars for the two variables are placed side-by-side. 3. Stacked bar charts, there the bars for each variable are placed upon each other. 4. Contingency tables – tables used to classify observations according to two identifiable characteristics. Example: A group of items are characterized by a certain attribute: X,Y, or Z, and according to the state in which they are produced. Contingency Table: X Y Z Total New York 20 5 5 30 California 10 10 5 25 Total 30 15 10 55 (a)create a side-by-side bar chart to compare the numbers of items of each type made in CA and NY. (b)Construct a stacked bar chart to compare the numbers of items of each type made in CA and NY. Side-by-side: 25 20 15 Frequency 10 NY CA 5 0 X Y Z category Stacked: 35 30 25 20 frequency 15 CA 10 NY 5 0 X Y Z category Section 2.2 Organizing Quantitative Data: Graphs for quantitative data 1. Frequency distribution 2. Relative frequency distribution 3. Histograms 4. Relative frequency histogram 5. Frequency polygons 6. Stem and Leaf plots Example: consider a sample of 42 randomly selected individuals from a sample population whose cholesterol level has been summarized in the following table: Classes (Cholesterol Frequencies Relative frequencies level) 0-199 13 32.5 % 200-399 11 27.5% 400-599 5 12.5% 600-799 8 20.0% 800-999 2 5% 1000-1199 0 0% 1200-1399 1 2.5% Total 42 100% Class width is the difference between two consecutive upper (or lower) class limits. Class width = Xmax – Xmin Number of classes OR Class width = [Xmax – Xmin/# of classes +1] where the brackets [x] = the greatest integer function (GIF) Example GIFs: [10] = 10 [9.9] = 9 [8.1] = 8 It is suggested that the number of classes k, should approximately satisfy : 2^(k-1) < n < 2^k where n is the total number of observations. A Histogram is a bar graph in which the horizontal axis represents classes of data values, and the vertical axis represents their frequencies (the bars should be adjacent to each other). A Relative Frequency Histogram is a bar graph in which the horizontal axis represents classes of data, and the vertical axis represents their relative frequencies (the bars should be adjacent to each other). Example: in a survey, 20 people were asked how many magazines they had purchased during the previous year. The results are: 6, 15, 3, 36, 25, 8, 12, 18, 5, 30, 24, 19, 4, 12, 9 (n=20) Construct a frequency distribution, a histogram, and a relative frequency histogram for this data: Xmin = 0 ; Xmax = 36 The number of classes should satisfy 2^(k-1) < 20 < 2^k Class width: [36-0/5 +1] = [8.2] = 8 Classes (# Frequency Relative Frequency magazines) 0 - 7 6 .3 8 - 15 5 .25 16 - 23 4 .2 24 - 31 4 .2 32 - 39 1 .05 SUM 20 1 Histogram: 7 6 5 4 Frequency 3 2 1 0 0 to 7 8 to 15 16 to 23 24 to 31 32 to 39 Classes Relative Frequency Histogram: 0.35 0.3 0.25 0.2 0.15 Relative Frequency 0.1 0.05 0 Classes A dot plot is a graph in which each data value is plotted as a point or a dot along a horizontal axis with marked values. 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5

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