exercises 4.17 - 4.33\n4.17 ● the following data are costs (in cents) per ounce for nine different brands of…

exercises 4.17 - 4.33\n4.17 ● the following data are costs (in cents) per ounce for nine different brands of sliced swiss cheese (consumerreports.org):\n29 62 37 41 70 82 47 52 49\na. calculate the variance and standard deviation for this data set. (hint: see example 4.8.)\nb. if a very expensive cheese with a cost per slice of $1.50 (150 cents) was added to the data set, how would the values of the mean and standard deviation change?

exercises 4.17 - 4.33\n4.17 ● the following data are costs (in cents) per ounce for nine different brands of sliced swiss cheese (consumerreports.org):\n29 62 37 41 70 82 47 52 49\na. calculate the variance and standard deviation for this data set. (hint: see example 4.8.)\nb. if a very expensive cheese with a cost per slice of $1.50 (150 cents) was added to the data set, how would the values of the mean and standard deviation change?

Answer

Explanation:

Step1: Calculate the mean

The data set is (29,62,37,70,82,47,52,49). The mean (\bar{x}=\frac{29 + 62+37+70+82+47+52+49}{8}=\frac{428}{8} = 53.5)

Step2: Calculate the squared - differences

((29 - 53.5)^2=(-24.5)^2 = 600.25), ((62 - 53.5)^2=(8.5)^2 = 72.25), ((37 - 53.5)^2=(-16.5)^2 = 272.25), ((70 - 53.5)^2=(16.5)^2 = 272.25), ((82 - 53.5)^2=(28.5)^2 = 812.25), ((47 - 53.5)^2=(-6.5)^2 = 42.25), ((52 - 53.5)^2=(-1.5)^2 = 2.25), ((49 - 53.5)^2=(-4.5)^2 = 20.25)

Step3: Calculate the variance

The variance (s^{2}=\frac{600.25+72.25 + 272.25+272.25+812.25+42.25+2.25+20.25}{8 - 1}=\frac{2094}{7}\approx299.14)

Step4: Calculate the standard deviation

The standard deviation (s=\sqrt{299.14}\approx17.30)

Step5: Add the new data point and calculate the new mean

The new data set is (29,62,37,70,82,47,52,49,150). The new mean (\bar{x}_{new}=\frac{29+62 + 37+70+82+47+52+49+150}{9}=\frac{578}{9}\approx64.22)

Step6: Calculate the new squared - differences

((29 - 64.22)^2=(-35.22)^2\approx1240.45), ((62 - 64.22)^2=(-2.22)^2\approx4.93), ((37 - 64.22)^2=(-27.22)^2\approx740.93), ((70 - 64.22)^2=(5.78)^2\approx33.41), ((82 - 64.22)^2=(17.78)^2\approx316.13), ((47 - 64.22)^2=(-17.22)^2\approx296.53), ((52 - 64.22)^2=(-12.22)^2\approx149.33), ((49 - 64.22)^2=(-15.22)^2\approx231.65), ((150 - 64.22)^2=(85.78)^2\approx7359.21)

Step7: Calculate the new variance

The new variance (s_{new}^{2}=\frac{1240.45+4.93+740.93+33.41+316.13+296.53+149.33+231.65+7359.21}{9 - 1}=\frac{10372.87}{8}=1296.61)

Step8: Calculate the new standard deviation

The new standard deviation (s_{new}=\sqrt{1296.61}\approx36.01) The mean increases from (53.5) to approximately (64.22) and the standard deviation increases from approximately (17.30) to approximately (36.01)

Answer:

a. Variance: approximately (299.14), Standard deviation: approximately (17.30) b. The mean increases from approximately (53.5) to approximately (64.22) and the standard deviation increases from approximately (17.30) to approximately (36.01)