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Ch. 12 Notes Pages 25 P25 12.4: Standard Deviation Measures of Central Tendency Mean, median, and mode: 98, 95, 99, 97, 89, 92, 97, 62, 90 Box-and-Whisker Plot Lower Extreme Lower Quartile Median Upper Quartile Upper Extreme Average temperatures of water in each month in Pensacola, FL (over 13 months) Jan: 56 Apr: 71 Jul: 84 Oct: 74 Feb: 58 May: 78 Aug: 86 Nov: 73 Mar: 63 Jun: 84 Sept: 82 Dec: 65 Jan: 58 Box-and-Whisker Plot ***List the data from least to greatest Median of upper part(Q3) Median of lower part (Q1) = 83 = 60.5 56, 58, 58, 63, 65, 71, 73, 74, 78, 82, 84, 84, 86 Median of data set (Q2) = 73 Standard Deviation Range: The difference between the greatest and least values Interquartile Range (IQR): The difference between the 3rd and 1st quartiles (Q3-Q1) Standard Deviation: How much the values in a data set vary from the mean ***The smaller the standard deviation, the closer all of the numbers are to the mean Standard Deviation Finding Standard Deviation: 1. Find the mean of the data set: x 2. Find the difference between each value and the mean: 3. Square each difference: x x xx 2 4. Find the average of these squares: x x 2 n 5. Take the square root to find standard deviation: ( x x) 2 n Standard Deviation 48.0, 53.2, 52.3, 46.6, 49.9 Finding Standard Deviation with the Calculator Daily Energy Demand during Weekends in August Step 1: Enter data into L1 Step 2: Use the CALC menu of STAT to access the 1-Var Stats option Ch. 12 Notes Page 26 P26 12.5: Working with Samples Samples and Populations Sample – gathers info from only part of a population Sample Proportion – the ratio an event occurs in sample size n x n, where x is the number of times Random Sample – all members of a population are equally likely to be chosen (so this is a good representation of the population) Ex: Students and international travel Sample: 350 students; 284 haven’t traveled internationally Sample proportion: Bias A news program reports on a proposed school dress code. The purpose of the program is to find out what percent of the population in its viewing area favors the dress code. Identify the bias in each sampling method: 1. Viewers are invited to call the program and express their preferences. “self-selected” 2. A reporter interviews people on the street near the local high school. “convenience” 3. During the program, 300 people are selected at random from the viewing area. “random” Margin of Error When a random sample of size n is taken from a large population, the sample proportion has a margin of error of about . 1 n ***The larger the sample, the smaller the margin of error! We use margin of error to give us an interval that is likely to contain the true population proportion Using the Margin of Error A recent poll of 75 people at the mall reported that 64 would rather shop at American Eagle than Eddie Bauer. 1. Sample Proportion 2. Margin of Error 3. Interval likely to contain the true population proportion 12.5 Working with Samples