University:
Glendale Community College
Course:
MAT 140 | College Mathematics
Academic year:

2020
Views:

194

Pages:

4
Author:

toonvalae

Homework #1-6: Determine the range and standard deviation of the set of data, round to the nearest hundredth when applicable. You may use your calculator to calculate standard deviation. Remember to select the “s”. 1) 10, 10, 14, 16, 8, 8 Mean = 10+10+14+16+8+8 6 = 11 Number Number - mean 10 10 14 16 8 8 Total 10 – 11 = -1 10 – 11 = -1 14 – 11 = 3 16 – 11 = 5 8 – 11 = - 3 8 – 11 = - 3 Squared difference (-1)2 = 1 (-1)2 = 1 (3)2 = 9 (5)2 = 25 (-3)2 = 9 (-3)2 = 9 1+1+9+25+9+9=54 I need to divide by the number of data points minus 1. I will divide by 6 – 1 = 5 54 Standard deviation = √ 5 = 3.286 Answer: Standard Deviation = 3.29 Range = 16 – 8 = 8 3) 50, 75, 100, 125, 150, 175, 200 Mean = 50+75+100+125+150+175+200 7 = 125 Number Number - mean 50 75 100 125 150 175 200 Total 50 – 125 = -75 75 – 125 = -50 100 – 125 = -25 125 – 125 = 0 150 – 125 = 25 175 – 125 = 50 200 – 125 = 75 Squared difference (-75)2 = 5625 (-50)2 = 2500 (-25)2 = 625 (0)2 = 0 (25)2 = 625 (50)2 = 2500 (75)2 = 5625 17500 I need to divide by the number of data points minus 1. I will divide by 7 – 1 = 6 17500 Standard deviation = √ 6 = 54.006 Answer: Standard Deviation = 54.01 Range = 200 – 50 = 150 5) 5, 10, 45, 200, 300, 400 Mean = 5+10+45+200+300+400 6 = 160 Number Number - mean 5 10 45 200 300 400 Total 5-160 = -155 10 – 160 = -150 45 – 160 = -115 200 – 160 = 40 300 – 160 = 140 400 – 160 = 240 Squared difference (-155)2 = 24025 (-150)2 = 22500 (-115)2 = 13225 (40)2 = 1600 (140)2 = 19600 (240)2 = 57600 138550 I need to divide by the number of data points minus 1. I will divide by 6 – 1 = 5 138550 Standard deviation = √ 5 = 166.463 Answer: Standard Deviation = 166.46 Range = 400 – 5 = 395 7) At the Steakhouse Grill, steaks are cut into 12‐ounce portions when they are ordered by a customer. For the past month, the manager of Steakhouse Grill has been trying to determine which cook can mostly accurately portion out the meat. The manager collected the mean of sample meat portions for a few weeks for both of his cooks. The results are summarized in the table below. Opie Maynard Week 1 12.5 12.0 Week 2 12.3 12.2 Week 3 11.8 11.8 Week 4 11.2 12.4 a) Compute the mean portion size for each cook. 12.5+12.3+11.8+11.2 Opie mean = = 11.95 𝑜𝑧 4 12.0+12.2+11.8+12.4 Maynard mean = = 12.1 𝑜𝑧 4 b) Compute the standard deviations for each cook. I used my calculator to find these standard deviations. See me if you can’t get the correct answer. I can show you how to use your calculator, or do it by hand. Opie Standard Deviation = .58 oz Maynard Standard Deviation = .26 oz c) The manager needs to choose a cook to cut portions of meat throughout the week. Who should he choose? Why? Maynard’s cuts are more consistent and closer to the desired average. I would pick Maynard. I could see an argument for Opie. If you selected Opie and gave a good reason, I would give you credit.