Pick 9 different dog breeds and find their average weights. List each breed and weight. Find the mean, median, and mode of the data. Which measure of central tendency best describes the data? Explain your answer.
How much would a 10th dog have to weight for the average weight in part (a) to be 250 pounds? Explain how you determined your answer.
1. Labrador Retriever - 65-80 pounds
2. English Mastiff - 120-230 pounds
3. Chihuahua - 3-6 pounds
4. Australian Shepherd - 40-65 pounds
5. Great Dane - 110-190 pounds
6. Beagle - 18-30 pounds
7. Yorkshire Terrier - 4-7 pounds
8. Rottweiler - 77-130 pounds
9. Shih Tzu - 9-16 pounds
Mean: (65+120+3+40+110+18+4+77+9)/9=47.7
Median: 40 (middle value when ordered from least to greatest)
Mode: No mode as no value appears more than once
The best measure of central tendency for this data is the median because it is not affected by outliers and the weights vary greatly between breeds.
To determine the weight of a 10th dog to make the average 250 pounds, we can use the formula: (current sum of weights + weight of 10th dog)/10 = 250
Simplifying the equation, we get: current sum of weights + weight of 10th dog = 2500
Assuming we want a dog breed that is not already listed, we can choose a Basset Hound with an average weight of 40-65 pounds.
Using the average weight of 52.5 pounds, we can plug it into the equation:
(current sum of weights + 52.5)/10 = 250
Solving for the current sum of weights, we get:
current sum of weights = 1947.5
Therefore, to have an average weight of 250 with a Basset Hound included, the 10th dog would need to weigh approximately 552.5 pounds.