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The least-squares principle Let us return to the sociologist interested in youth culture

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The least-squares principle Let us return to the sociologist interested in youth culture. He is conducting research on Facebook. To determine how many Facebook friends students have, he obtains a sample of nine students. Students are asked how many Facebook friends they have. Their responses are shown in the table that follows: Number of Social Networking Friends Student Social Networking Friends 1 223 653 125 64 43 141 82 141 OOONGU'I-PKUJN 112 Calculate the mean, the median, and the mode of the sample, and then enter each value in the appropriate box. Mean = Median =

Complete the table by selecting from the dropdown menus the correct squared variation from the mean, the median, and the mode for 223 and 653: Distances from the Different Measurements of Central Tendency X, (Student) (X, — {)2 (X, — Md)2 (X, — Mode)2 43 (5) 17,689 6,724 9,604 64 (4) 12,544 3,721 5,929 82 (7) 8,836 1,849 3,481 112 (9) 4,096 169 841 125 (3) 2,601 0 256 141 (6) 1,225 256 0 141 (8) 1,225 256 o 223 (1) v v v 653 (2) v v v 2 (X,- —§)2 = v 201.- — Md)2 = v 201,- — Mode)2 = v Complete the table by selecting in the dropdown menus the correct sum of the squared variation from the mean, the median, and the mode. The measure of central tendency that is the closest to all the other scores is the V .

The mean is the average score V . Suppose you are a sociologist doing a telephone study on criminal activity in the Detroit area. You collect demoglaphic data on the people you interview, including their addresses and phone numbers. What is wrong with calculating the mean of the area code data? C The median is the more appropriate statistic for area codes. A Area codes are nominal data, not numerical. A There is nothing wrong with calculating the mean of the area code data. Suppose you collect a sample of 1,000 people. For each person in your sample, you have measured a value for each of the variables listed in the ?rst column of the following table. For each variable, select which of the measures of central tendency are supposed to be used to describe your sample's values for that variable. Check all that apply. Variable Description Mode Median Mean Gender (3 [3 Height in inches Level of schooling completed (did not complete high school, high school graduate, college graduate, postgraduate ? degree) Note that the mean is not supposed to be used with variables measured at the ordinal v level but commonly is because the mean is much more flexible than the median. The presence of extremely large or small values in the data affects the mean more V than the median. Therefore, the median V is the preferred measure of central tendency when the distribution has notable outlying scores.

The following are weights (in pounds) for a sample of 12 baby girls at the age of 21 months: Weights of 21-Month-Old Baby Girls Baby Weight 1 21.9 2 22.2 3 23.1 4 24.4 5 25.7 26.3 7 27.5 8 28.6 9 29.8 10 31.5 11 33.1 12 34.2 N = 12 The 1st quartile for the sample data is pounds, the 2nd quartile is pounds, and the 3rd quartile is pounds. The 1st decile for the sample data is pounds, the 5th decile is pounds, and the 9th decile is pounds.

Occasionally with statistics, but particularly with measures of position, you can have multiple terms for the same thing. For example, which of the following terms are equivalent to the 2nd quartile? Check all that apply. The 50th decile O D5 The 50th percentile O The mode