Chapter 2. Exploring Data with Graphs and Numerical Summaries. Learn. The Different Types of Data. The Use of Graphs to Describe Data
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1 Chapter 2 Exploring Data with Graphs and Numerical Summaries Learn. The Different Types of Data The Use of Graphs to Describe Data The Numerical Methods of Summarizing Data Agresti/Franklin Statistics, 1of 63
2 Graphs and Numerical Summaries Describe the main features of a variable For Quantitative variables: key features are center and spread For Categorical variables: key feature is the percentage in each of the categories Agresti/Franklin Statistics, 2of 63
3 Frequency Table A method of organizing data Lists all possible values for a variable along with the number of observations for each value Agresti/Franklin Statistics, 3of 63
4 Example: Shark Attacks Agresti/Franklin Statistics, 4of 63
5 Example: Shark Attacks What is the variable? Is it categorical or quantitative? How is the proportion for Florida calculated? How is the % for Florida calculated? Which region is the most frequent attacked? Agresti/Franklin Statistics, 5of 63
6 Example: Shark Attacks Insights what the data tells us about shark attacks How many time sharks attacks occurred in each region. The variable here is the region in which each observation (shark attach) took place. Agresti/Franklin Statistics, 6of 63
7 Section 2.2 How Can We Describe Data Using Graphical Summaries? Agresti/Franklin Statistics, 7of 63
8 Graphs for Categorical Data Pie Chart: A circle having a slice of pie for each category Bar Graph: A graph that displays a vertical bar for each category Agresti/Franklin Statistics, 8of 63
9 Example: Sources of Electricity Use in the U.S. and Canada Agresti/Franklin Statistics, 9of 63
10 Pie Chart Agresti/Franklin Statistics, 10 of 63
11 Bar Chart Agresti/Franklin Statistics, 11 of 63
12 Pie Chart vs. Bar Chart Which graph do you prefer? Both are simple to construct using software Bar chart is more precise and more flexible Bar chart can be used for comparison Agresti/Franklin Statistics, 12 of 63
13 Graphs for Quantitative Data Dot Plot: shows a dot for each observation Stem-and-Leaf Plot: portrays the individual observations Histogram: uses bars to portray the data Agresti/Franklin Statistics, 13 of 63
14 Example: Sodium and Sugar Amounts in Cereals Agresti/Franklin Statistics, 14 of 63
15 Dotplot for Sodium in Cereals Sodium Data: Agresti/Franklin Statistics, 15 of 63
16 Stem-and-Leaf Plot for Sodium in Cereal Sodium Data: Agresti/Franklin Statistics, 16 of 63
17 Frequency Table Sodium Data: Agresti/Franklin Statistics, 17 of 63
18 Histogram for Sodium in Cereals Agresti/Franklin Statistics, 18 of 63
19 Which Graph? Dot-plot and stem-and-leaf plot: More useful for small data sets Data values are retained Histogram More useful for large data sets Most compact display More flexibility in defining intervals Agresti/Franklin Statistics, 19 of 63
20 Shape of a Distribution Overall pattern Clusters? Outliers? Symmetric? Skewed? Unimodal? Bimodal? Agresti/Franklin Statistics, 20 of 63
21 Symmetric or Skewed? Agresti/Franklin Statistics, 21 of 63
22 Example: Hours of TV Watching Skewed to the right Agresti/Franklin Statistics, 22 of 63
23 Identify the minimum and maximum sugar values: a. 2 and 14 b. 1 and 3 c. 1 and 15 d. 0 and 16 Agresti/Franklin Statistics, 23 of 63
24 Consider a data set containing IQ scores for the general public: What shape would you expect a histogram of this data set to have? a. Symmetric b. Skewed to the left c. Skewed to the right d. Bimodal Agresti/Franklin Statistics, 24 of 63
25 Consider a data set of the scores of students on a very easy exam in which most score very well but a few score very poorly: What shape would you expect a histogram of this data set to have? a. Symmetric b. Skewed to the left c. Skewed to the right d. Bimodal Agresti/Franklin Statistics, 25 of 63
26 Section 2.3 How Can We describe the Center of Quantitative Data? Agresti/Franklin Statistics, 26 of 63
27 Mean The sum of the observations divided by the number of observations x = x n Agresti/Franklin Statistics, 27 of 63
28 Median The midpoint of the observations when they are ordered from the smallest to the largest (or from the largest to the smallest) Agresti/Franklin Statistics, 28 of 63
29 Find the mean and median CO 2 Pollution levels in 8 largest nations measured in metric tons per person: a. Mean = 4.6 Median = 1.5 b. Mean = 4.6 Median = 5.8 c. Mean = 1.5 Median = 4.6 Mean=( )/8=36.8/8=4.6- (a) or (b) Median Step 1: sort the data: 0.2, 0.7, 1.1, 1.2, 1.8, 2.3, 9.8, 19.7 Step 2: if n (=8) is even, then average the middle two values=median ( )/2=1.5 Agresti/Franklin Statistics, 29 of 63
30 Answer: (a) Mean=( )/8=36.8/8=4.6 (a) or (b) Median Step 1: sort the data: 0.2, 0.7, 1.1, 1.2, 1.8, 2.3, 9.8, 19.7 Step 2: if n (=8) is even, then average the middle two values=median Median=( )/2=1.5, hence (a). Agresti/Franklin Statistics, 30 of 63
31 Outlier An observation that falls well above or below the overall set of data The mean can be highly influenced by an outlier The median is resistant: not affected by an outlier Agresti/Franklin Statistics, 31 of 63
32 Mode The value that occurs most frequently. The mode is most often used with categorical data Agresti/Franklin Statistics, 32 of 63
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