The data pairs in the table are from 600 matched pairs of magnitude/depth measurements randomly selected from 10,594 earthquakes recorded in one year from a location in southern California. Only earthquakes with a magnitude of at least 1.00 are used. MAGNITUDE is magnitude measured on the Richter scale and DEPTH is depth in kilometers (km). The magnitude and depth both describe the source of the earthquake. The data are from the Southern California Earthquake Data Center. Use the table data to do the following: 1) Construct a histogram of the magnitudes. Use a class width of 0.50 and use a starting value of 1.00. Easy instructions for using a spreadsheet (they show Excel, but you may use Google Sheets) can be found here. You must upload your spreadsheet. You may not use AI, such as ChatGPT, etc. (15 points) 2) Looking at your histogram, which of the following comes close to describing the distribution: uniform, normal, skewed left, or skewed right? Briefly explain your choice. (5 points) 3) Consider the earthquake depths (in kilometers). a) Are the depth data categorical or quantitative? How do you know? (5 points) b) The depths are all rounded to one decimal place. Before rounding, are the exact depths that were measured discrete data or continuous data? How do you know? (5 points) c) Given that the listed earthquake depths are part of a larger collection of depths, do the data constitute a sample or population? Briefly explain your answer. (5 points) 4) Consider the paired magnitude/depth data. 2.45 MAGNITUDE DEPTH 0.7 3.62 3.06 6.0 7.0 3.3 1.09 5.4 0.5 3.1 2.99 17.6 0.0 7.0 2.58 2.44 2.91 7.0 15.9 3.38 2.83 11.7 7.0 2.44 2.56 7.0 2.79 6.9 17.3 2.18 3.01 7.0 7.0 2.71 2.44 7.0 7.0 8.1 1.64 a) Construct a scatterplot to determine whether there is a correlation between earthquake magnitudes and depths. Feel free to use a spreadsheet. However I encourage you to use Desmos as demonstrated in the notes. You may not use AI, such as ChatGPT, etc. You must turn in your scatterplot. If you use Desmos, click the Share icon and choose Share a Snapshot. A custom URL web address will be created for you to copy and paste. If you use Excel or Google Sheets, upload your file. (5 points) b) What is the correlation coefficient? Based on the result, does there appear to be a correlation? Briefly explain your answer. (10 points)
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