IPS6eCh01_2bb

# IPS6eCh01_2bb - Looking at Data Distributions Describing...

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Looking at Data - Distributions Describing distributions with numbers IPS Chapter 1.2

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Review Selected Terms from Section 1.1 Observation = Individual = Case Variable: Categorical versus Quantitative Frequency (= counts) and relative frequency (percents or fractions) Bar graph, pie chart, stemplot (or stem and leaf diagram), and histogram. Distributions: shape center and spread Shapes: symmetric, skewed, bi- (or multi-) modal Outliers Time plot, trend, seasonal fluctuations Time series versus cross section data
Sometimes the data are better represented by one type of chart or graph than another: The breakdown of GDP into C + I + G + NX (net exports) is often shown in pie charts – but the fact that NX is negative is hard to show. Bar charts can show how values of quantitative variables differ for observations with different categorical variable values. For example, how the number and proportion of workers earning over \$50,000 is greater for men than for women. Histograms are best used when the variable of primary interest is quantitative and where observations can easily be put into categories of equal size. For example, the count or percentage of a class of students who have sample that has scores between 50- 60%, 60-70%. ..90-100%. It is difficult to create a histogram of income earned by people in a sample where the intervals are \$10,000. Some individuals will have very high income – so to include them many empty categories must be included. (e.g., must have 980,000-990,000 and 990,000-1,000,000 to include one millionaire in category: 1,000,000-1,010,000 ).

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Objectives (IPS Chapter 1.2) Describing distributions with numbers Measures of center: mean, median Mean versus median Measures of spread: quartiles, standard deviation Five-number summary and boxplot Choosing among summary statistics Changing the unit of measurement
The mean or arithmetic average To calculate the average, or mean, add all values, then divide by the number of individuals. It is the “center of mass.” Sum of heights is 1598.3 divided by 25 women = 63.9 inches 58.2 64.0 59.5 64.5 60.7 64.1 60.9 64.8 61.9 65.2 61.9 65.7 62.2 66.2 62.2 66.7 62.4 67.1 62.9 67.8 63.9 68.9 63.1 69.6 63.9 Measure of center: the  mean

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x = 15 98 .3 25 = 63 .9 Mathematical notation: = = n i i x n x 1 1 w o ma n ( i ) h ei gh t ( x ) w o ma n ( i ) h ei gh t ( x ) i = 1 x 1 = 5 8 . 2 i = 14 x 14 = 6 4 . 0 i = 2 x 2 = 5 9 . 5 i = 15 x 15 = 6 4 . 5 i = 3 x 3 = 6 0 . 7 i = 16 x 16 = 6 4 . 1 i = 4 x 4 = 6 0 . 9 i = 17 x 17 = 6 4 . 8 i = 5 x 5 = 6 1 . 9 i = 18 x 18 = 6 5 . 2 i = 6 x 6 = 6 1 . 9 i = 19 x 19 = 6 5 . 7 i = 7 x 7 = 6 2 . 2 i = 20 x 20 = 6 6 . 2 i = 8 x 8 = 6 2 . 2 i = 21 x 21 = 6 6 . 7 i = 9 x 9 = 6 2 . 4 i = 22 x 22 = 6 7 . 1 i = 10 x 10 = 6 2 . 9 i = 23 x 23 = 6 7 . 8 i = 11 x 11 = 6 3 . 9 i = 24 x 24 = 6 8 . 9 i = 12 x 12 = 6 3 . 1 i = 25 x 25 = 6 9 . 6 i = 13 x 13 = 6 3 . 9 n = 2 5 Σ = 1 5 9 8 . 3 Learn right away how to get the mean using your calculators.
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IPS6eCh01_2bb - Looking at Data Distributions Describing...

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