(PLEASE HELP 50 POINTS) At a dog show, the entries included Welsh corgis and cocker spaniels. The table compares the weights within this sample of dogs. Mean
(pounds)
Median
(pounds)
Range
(pounds)
MAD
(pounds)
Welsh corgi
27.3
27
7
2.3
Cocker spaniel
27.3
27.5
2
0.8

Answer the questions to compare the weights of the dog breeds and determine which breed of dog had the heaviest entry.

1. What is the median weight of the Welsh corgis? What does the median tell you about their weights?

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2. Which type of dog has the greater variation in weights? Justify your answer.

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3. Do you think the heaviest dog in the show was a Welsh corgi or a cocker spaniel? Explain how you made your choice.

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Each of the following data sets has a mean of x = 10. (i) 8 9 10 11 12 (ii) 7 9 10 11 13 (iii) 7 8 10 12 13 (a) without doing any computations, order the data sets according to increasing value of standard deviations. (i), (iii), (ii) (ii), (i), (iii) (iii), (i), (ii) (iii), (ii), (i) (i), (ii), (iii) (ii), (iii), (i) (b) why do you expect the difference in standard deviations between data sets (i) and (ii) to be greater than the difference in standard deviations between data sets (ii) and (iii)? hint: consider how much the data in the respective sets differ from the mean. the data change between data sets (i) and (ii) increased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). the data change between data sets (ii) and (iii) increased the squared difference îł(x - x)2 by more than data sets (i) and (ii). the data change between data sets (i) and (ii) decreased the squared difference îł(x - x)2 by more than data sets (ii) and (iii). none of the above