Which team seems to have more variability, the Astros or the Dodgers?

Learning Goal: I’m working on a research & summaries question and need a sample draft to help me learn.In baseball, a player’s “batting average” is one way to measure how well a player is batting that season. It is calculated from the number of times they hit the ball and get on a base (hits) divided by the number of total times they were at bat (a higher batting average is a good thing–if a player has a higher batting average it means they were able to get on base more, they struck out less). Below are the batting averages of 15 players from the LA Dodgers and Houston Astros from 2021 regular season (these are real data from this season!). Batting Averages for 15 Dodgers Players: Batting Averages for 15 Astros Players: 0.2490.277 0.2780.278 0.2580.294 0.2640.279 0.2970.319 0.2540.257 0.3060.27 0.2540.172 0.1650.311 0.3380.235 0.270.259 0.2420.26 0.2150.211 0.2150.304 0.1690.176 Question 1 Using the data provided, what is the mean for the “batting average” of the 15 Dodgers players?Round your answer to three decimal places. Question 2 Using the data provided, what is the variance of the “batting average” for the 15 Dodgers players?Round your answer to three decimal places. Question 3 Using the data provided, what is the standard deviation of the “batting average” for the 15 Dodgers players?Round your answer to three decimal places. Question 4 Using the data provided, what is the mean “batting average” for the 15 Astros players?Round your answer to three decimal places. Question 5 Using the data provided, what is the variance of the “batting average” for the 15 Astros players?Round your answer to three decimal places. Question 6 Using the data provided, what is the standard deviation of the “batting average” for the 15 Astros players?Round your answer to three decimal places. Question 7 Show your work here! Upload a picture or file of your work for the calculation of the variance and SD for both groups. You can upload one (or multiple) pictures. To upload a file click on the three dots on the menu below, then click on the “picture icon” and then click “upload image”.A photo of your hand calculations and “the table” you used to calculate them would be sufficient! If you are using an iphone, please convert your image to a .jpeg or .docx format (you can paste the image into a word document and submit that). If you submit using the .HEIC format, we will be unable to read your answer. Remember, your table for calculations should look something like this: X X-M (X-M)2 ∑ Question 8 Which team seems to have more variability, the Astros or the Dodgers? (careful: they’re very close!). Neither team has any variability
Astros
Dodgers
Question 9 Which team has the higher mean? neither team has a higher mean
Dodgers
Astros
Question 10 The Dodgers are considering bringing a new player onto their team. This new player has a batting average of 0.271. Is this new player’s batting average within one standard deviation (above or below) the mean for the Dodgers? Why or why not? (note: you do not need to recalculate the mean and SD for this group with the new player, simply compare this new player to the existing team) Question 11 Based on the new player’s batting average (the one from the question above), should the Dodgers bring this person onto the team? Why or why not? Explain.
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