Assume you have a set of n scalar observations {1,2,...,n} CR. An important, basic data analysis...

 

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Assume you have a set of n scalar observations {1,2,...,n} CR. An important, basic data analysis task would be to summarize these observations in a single number that captures the "middle" of the dataset. Two choices are the median, which we'll call , and the mean, which we'll call 2. The definition of mean is, and the definition of median is in the book. 1. /5 points) Compute 1 and 2 for the dataset (2,5, 3, 7, 4, 3.5, 25), and plot the dataset, #1, and 2 on a number line. 2. [5 points] Show that the median minimizes the cost function TL -. i=1 You can assume that n is odd. (Hints: Show that for any up, the cost decreases as you move to the right or left. You may also make an argument using calculus, although keep in mind that the absolute value function isn't differentiable everywhere.) Assume you have a set of n scalar observations {1,2,...,n} CR. An important, basic data analysis task would be to summarize these observations in a single number that captures the "middle" of the dataset. Two choices are the median, which we'll call , and the mean, which we'll call 2. The definition of mean is, and the definition of median is in the book. 1. /5 points) Compute 1 and 2 for the dataset (2,5, 3, 7, 4, 3.5, 25), and plot the dataset, #1, and 2 on a number line. 2. [5 points] Show that the median minimizes the cost function TL -. i=1 You can assume that n is odd. (Hints: Show that for any up, the cost decreases as you move to the right or left. You may also make an argument using calculus, although keep in mind that the absolute value function isn't differentiable everywhere.)