Questions: House prices: The following table presents prices, in thousands of dollars, of single-family homes for 20 of the 25 largest metropolitan areas in the United States for last year and this year. Metro Area, Last year, This year Boston, MA, 311.5, 332.2 Chicago, IL., 157.2, 159.4 Cincinnati, OH, 112.5, 121.0 Cleveland, OH, 84.9, 101.0 Dallas, TX, 148.2, 160.4 Denver, CO, 226.4, 261.2 Houston, TX, 152.1, 163.7 Los Angeles, CA, 122.1, 155.1 Miami, FL, 182.0, 219.9 Minneapolis, MN, 147.3, 170.6 New York, NY, 363.8, 368.2 Philadelphia, PA, 193.5, 197.7 Phoenix, AZ, 129.9, 169.0 Portland, OR, 208.6, 246.5 Riverside, CA, 174.3, 216.7 San Diego, CA, 359.5, 412.3 San Francisco, CA, 448.0, 593.9 Seattle, WA, 265.4, 312.6 St. Louis, MO, 103.7, 111.0 Tampa, FL, 131.9, 141.8 (a) Find the mean and median price for last year. Last year, the mean price, in thousands of dollars, was 201.14 and the median price, in thousands of dollars, was 165.75. (b) Find the mean and median price for this year. This year, the mean price, in thousands of dollars, was 230.71 and the median price, in thousands of dollars, was 184.15. (c) In general, house prices increased from last year to this year. Which increased more, the mean or the median?

House prices: The following table presents prices, in thousands of dollars, of single-family homes for 20 of the 25 largest metropolitan areas in the United States for last year and this year. Metro Area, Last year, This year Boston, MA, 311.5, 332.2 Chicago, IL., 157.2, 159.4 Cincinnati, OH, 112.5, 121.0 Cleveland, OH, 84.9, 101.0 Dallas, TX, 148.2, 160.4 Denver, CO, 226.4, 261.2 Houston, TX, 152.1, 163.7 Los Angeles, CA, 122.1, 155.1 Miami, FL, 182.0, 219.9 Minneapolis, MN, 147.3, 170.6 New York, NY, 363.8, 368.2 Philadelphia, PA, 193.5, 197.7 Phoenix, AZ, 129.9, 169.0 Portland, OR, 208.6, 246.5 Riverside, CA, 174.3, 216.7 San Diego, CA, 359.5, 412.3 San Francisco, CA, 448.0, 593.9 Seattle, WA, 265.4, 312.6 St. Louis, MO, 103.7, 111.0 Tampa, FL, 131.9, 141.8 (a) Find the mean and median price for last year. Last year, the mean price, in thousands of dollars, was 201.14 and the median price, in thousands of dollars, was 165.75. (b) Find the mean and median price for this year. This year, the mean price, in thousands of dollars, was 230.71 and the median price, in thousands of dollars, was 184.15. (c) In general, house prices increased from last year to this year. Which increased more, the mean or the median?
Transcript text: House prices: The following table presents prices, in thousands of dollars, of single-family homes for 20 of the 25 largest metropolitan areas in the United States for last year and this year. Metro Area & Last year & This year \\ Boston, MA & 311.5 & 332.2 \\ Chicago, IL. & 157.2 & 159.4 \\ Cincinnati, OH & 112.5 & 121.0 \\ Cleveland, OH & 84.9 & 101.0 \\ Dallas, TX & 148.2 & 160.4 \\ Denver, CO & 226.4 & 261.2 \\ Houston, TX & 152.1 & 163.7 \\ Los Angeles, CA & 122.1 & 155.1 \\ Miami, FL & 182.0 & 219.9 \\ Minneapolis, MN & 147.3 & 170.6 \\ New York, NY & 363.8 & 368.2 \\ Philadelphia, PA & 193.5 & 197.7 \\ Phoenix, AZ & 129.9 & 169.0 \\ Portland, OR & 208.6 & 246.5 \\ Riverside, CA & 174.3 & 216.7 \\ San Diego, CA & 359.5 & 412.3 \\ San Francisco, CA & 448.0 & 593.9 \\ Seattle, WA & 265.4 & 312.6 \\ St. Louis, MO & 103.7 & 111.0 \\ Tampa, FL & 131.9 & 141.8 \\ (a) Find the mean and median price for last year. Last year, the mean price, in thousands of dollars, was 201.14 and the median price, in thousands of dollars, was 165.75. (b) Find the mean and median price for this year. This year, the mean price, in thousands of dollars, was 230.71 and the median price, in thousands of dollars, was 184.15. (c) In general, house prices increased from last year to this year. Which increased more, the mean or the median?
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Solution

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Solution Steps

Solution Approach
  1. Extract the house prices for last year and this year from the given data.
  2. Calculate the mean for both last year and this year by summing the prices and dividing by the number of data points.
  3. Calculate the median for both last year and this year by sorting the prices and finding the middle value.
  4. Compare the increase in mean and median from last year to this year to determine which increased more.
Step 1: Calculate the Mean and Median for Last Year

The mean price for last year is calculated as: \[ \text{mean\_last\_year} = 174.435 \] The median price for last year is: \[ \text{median\_last\_year} = 158.3 \]

Step 2: Calculate the Mean and Median for This Year

The mean price for this year is calculated as: \[ \text{mean\_this\_year} = 237.0105 \] The median price for this year is: \[ \text{median\_this\_year} = 197.7 \]

Step 3: Determine the Increase in Mean and Median

The increase in the mean price from last year to this year is: \[ \text{mean\_increase} = 62.5755 \] The increase in the median price from last year to this year is: \[ \text{median\_increase} = 39.4 \]

Step 4: Compare the Increases

Since \( \text{mean\_increase} = 62.5755 \) is greater than \( \text{median\_increase} = 39.4 \), the mean increased more than the median.

Final Answer

The mean increased more from last year to this year. \(\boxed{\text{mean}}\)

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