Final answer:
The mean, median, and mode of the given dog weights are calculated to be 53.63 lbs, 7.5 lbs, and 7 lbs respectively. To determine the weight of the 10th dog for the average weight to be 250 lbs, the weight of the other 9 dogs is subtracted from the total weight of 2500 lbs.
Step-by-step explanation:
To find the mean, median, and mode of the given dog weights, we can calculate:
Mean = (sum of all weights) / (number of weights)
= (55+15+7+150+2+5+120+75) / 8 = 429 / 8 = 53.63 lbs
Median = the middle value of the sorted weights = 7.5 lbs
Mode = the most frequent value = 7 lbs
To determine the weight of the 10th dog for the average weight to be 250 lbs, we need to find the total weight of all 10 dogs and then solve for the weight of the 10th dog:
Total weight = average weight * number of dogs = 250 lbs * 10 = 2500 lbs
Weight of 10th dog = total weight - sum of weights of the other 9 dogs
= 2500 lbs - (55+15+7+150+2+5+120+75+X) = 2500 lbs - (429 + X) = 2071 lbs - X
Therefore, the 10th dog would have to weigh 2071 lbs - X in order for the average weight to be 250 lbs.
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