Questions by rgrant - Page 25
Question 1The data given represents the number of gallons of coffee sold per hour at two different coffee shops.Perks A Lot10 3.5 35 2.5 78 5.5 9.56 9 4.5Wide Awake2.5 10 418 4 33 6.5 156 5 2.5Compare the data and use the correct measure of center to determine which shop typically sells the most amount of coffee per hour. Explain. Perks A Lot, with a median value of 5.75 gallons Wide Awake, with a median value of 4.5 gallons Perks A Lot, with a mean value of 5.75 gallons Wide Awake, with a mean value of 4.5 gallonsQuestion 2The line plots represent data collected on the travel times to school from two groups of 15 students.A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4,6,14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9,18, 20, and 22. There are two dots above 6, 10, 12,14, and 16. The graph is titled Bus 18 Travel Times.Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer. Bus 18, with an IQR of 16 Bus 47, with an IQR of 24 Bus 18, with a range of 16 Bus 47, with a range of 24Question 3The box plots display measures from data collected when 20 people were asked about their wait time at a drive-thru restaurant window.A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 8.5 to 15.5 on the number line. A line in the box is at 12. The lines outside the box end at 3 and 27. The graph is titled Super Fast Food.A horizontal line starting at 0, with tick marks every one-half unit up to 32. The line is labeled Wait Time In Minutes. The box extends from 9.5 to 24 on the number line. A line in the box is at 15.5. The lines outside the box end at 2 and 30. The graph is titled Burger Quick.Which drive-thru is able to estimate their wait time more consistently and why? Burger Quick, because it has a smaller IQR Burger Quick, because it has a smaller range Super Fast Food, because it has a smaller IQR Super Fast Food, because it has a smaller rangeQuestion 4The data given represents the height of basketball players, in inches, on two different girls' teams.Allstars73 62 6063 72 6569 68 7166 70 6760 70 71Super Stars66 68 6263 47 6465 50 6064 65 6558 60 55Compare the data and use the correct measure of center to determine which team typically has the tallest players. Explain your answer. The Allstars, with a mean of about 67.1 inches The Super Stars, with a mean of about 60.8 inches The Allstars, with a median of 68 inches The Super Stars, with a median of 63 inchesQuestion 5The histograms display the frequency of temperatures in two different locations in a 30-day period.A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. A shaded bar stops at 10 above 60 to 69, at 9 above 70 to 79, at 5 above 80 to 89, at 4 above 90 to 99, and at 2 above 100 to 109. There is no shaded bar above 110 to 119. The graph is titled Temps in Sunny Town.A graph with the x-axis labeled Temperature in Degrees, with intervals 60 to 69, 70 to 79, 80 to 89, 90 to 99, 100 to 109, 110 to 119. The y-axis is labeled Frequency and begins at 0 with tick marks every one unit up to 14. There is no shaded bar above 60 to 69. A shaded bar stops at 4 above 70 to 79, at 4 above 80 to 89, at 6 above 90 to 99, at 6 above 100 to 109 and at 10 above 110 to 119. The graph is titled Temps in Beach Town.When comparing the data, which measure of variability should be used for both sets of data to determine the location with the most consistent temperature? IQR, because Sunny Town is symmetric IQR, because Beach Town is skewed Range, because Sunny Town is skewed Range, because Beach Town is symmetricQuestion 6The stem-and-leaf plot displays data collected on the size of 15 classes at two different schools.Mountain View School Seaside School 0 5, 89, 8, 2, 0 1 0, 1, 2, 5, 6, 88, 7, 6, 5, 5, 4, 4, 3, 1, 0 2 5, 5, 7, 7, 80 3 0, 6Key: 2 | 1 | 0 means 12 for Mountain View and 10 for SeasidePart A: Calculate the measures of center. Show all work. (2 points)Part B: Calculate the measures of variability. Show all work. (1 point)Part C: If you are interested in a smaller class size, which school is a better choice for you? Explain your reasoning. (1 point)
Investigating the method of Gradient Descent.(ix) Now consider the general formula for the method of gradient descent for a function g(x,y): an+1 an 7Vg(an) Here v is a step size, and we must start with an initial location of o. The method of gradient descent is an algorithm that generates a sequence of points that, under the appropriate conditions, will converge to the location of a local minimum of the function g. Give a short explanation for why this algorithm will find the location of the minimum. You might mention what problems one might encounter. For example, what can go wrong with y? (x) Returning the functions f(x, y) and L(x, y) = ||f(x, y)||?, explain why we can't use the method of gradient descent on f(x, y), but why we can use it on L(x, y). (xi) Our goal with this project is to find the (x, y) pair(s) that make the function f(x, y) = (0,0). Explain why the results of applying the method of gradient descent on L(x, y) gives us just that. (xii) Provided is python code to implement the method of gradient descent for the function .5 L(x, y), using the initial point and a step size of y=.01. Further instructions .5 will be given in the code provided. (-5 (xiii) Use the result of the previous step (the python code) to estimate a point (x,y) that makes f(x, y) = 0. Verify that your guess makes f(x, y) = 0.