Chap 1 Overview and Descriptive Statistics Student.pdf

Simple random sampling a simple random sample srs of

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Simple Random Sampling A simple random sample (SRS) of size n consists of n individuals or objects from the population chosen in such a way that every possible collection of n individuals or objects is equally likely to selected. Example:
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Summary Statistics Notation: 𝑥 𝑛 𝑥 1 , 𝑥 2 , … , 𝑥 𝑛 𝑥 𝑖 𝑛 𝑖=1 = Summarizing Quantitative Data: Measures of Center: The _____________________________ is the numerical average of all the observations and is denoted by ______. The ___________________________ is the middle number when the observations are ordered from smallest to largest; it is denoted by ______. The ______________________________ is the most frequent observation.
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Example: Below is a random sample of 20 wait times for callers to the IRS. Find the mean and median. 12 61 15 2 45 8 5 23 18 37 4 20 8 9 19 33 19 22 9 31 In order, 2 4 5 8 8 9 9 12 15 18 19 19 20 22 23 31 33 37 45 61 Measures of Spread: The __________________________ is the difference between the largest and the smallest observations. ____________________________________________________ is the range of the middle 50% of the data. The _____________________________________ is the sum of the squared deviations of the observations from the sample mean and is denoted by ______. The p th percentile is a number p such that ________________ of the data is ____________________. Five Number Summary: Example: In addition to the sample of 20 above, two more samples of size 20 were taken. The data sets are summarized below. Sample 1: 2 4 5 8 8 9 9 12 15 18 19 19 20 22 23 31 33 37 45 61 Sample 2: 1 2 5 6 6 8 9 9 10 10 13 18 22 26 30 49 50 53 55 72 Sample 3: 1 3 5 5 7 8 10 11 12 16 19 21 23 25 26 45 45 53 61 72 Sample Min Q1 Median Q3 Max Mean Variance SD 1 2.00 8.75 18.50 25.00 61.00 20.00 227.79 15.09 2 1.00 7.50 11.50 34.75 72.00 22.70 457.59 21.39 3 1.00 7.75 17.50 30.75 72.00 23.40 433.62 20.82 Note: The population values are as follows:
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Types of Displays: 1. Line Graph Shows how the values of the variable change over time.
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