A specialty foods company sells "gourmet hams" by mail order. The hams vary in size from 4.15 to 7.45 pounds, with a mean weight of 6 pounds and standard deviation of 0.65 pounds. The quartiles and median weights are 5.6, 6.2, and 6.55 pounds.

a) Find the range and the IQR of the weights.

b) Do you think the distribution of the weights is symmetric or skewed? If skewed, which way? Why?

c) If these weights were expressed in ounces ( 1 pound = 16 ounces) what would the mean, standard deviation, quartiles, median, IQR, and range be?

d) When the company ships these hams, the box and packing materials add 30 ounces. What are the mean, standard deviation, quartiles, median , IQR, and range of weights of boxes shipped (in ounces)?

e) One customer made a special order of a 10-pound ham. Which of the summary statistics of part d might not change if that data value were added to the distribution?

Step-by-step explanation:

a) the range is the difference between the highest and lowest value:

range =7.5-4.15 =3.3 pounds

the IQR is the difference between the third and first quartile

IQR= Q₃ -Q₁ =6.55 - 5.6 = 0.95 Pounds

b) Skewed because the mean and median are not the same value.

c) All values will be multiplied by 16

  Mean: 96 ounce

  Standard deviation: 10.4 ounce

  Quartiles: 89.6 ounce and 104.8 ounce

  Median:99.2 ounce

  IQR: 15.2 ounce

  Range: 52.8 ounce

d) The mean,quartiles and median increase by 30,the result remain unchanged:

   Mean: 126 ounce

  Standard deviation: 10.4 ounce

  Quartiles: 119.6 ounce and 134.8 ounce

  Median:129.2 ounce

  IQR: 15.2 ounce

  Range: 52.8 ounce

e)  The median, quartiles and IQR might not changed,because they are unaffected by an outlier.

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step-by-step explanation:

table 3 represents a direct variation function. : )