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. Bulldog - 40-50 pounds
3. Siberian Husky - 35-60 pounds
4. Golden Retriever - 55-75 pounds
5. Poodle - 6-70 pounds
6. Dalmatian - 45-70 pounds
7. Boxer - 50-70 pounds
8. German Shepherd - 50-90 pounds
9. Beagle - 18-30 pounds
Mean: (65+45+35+55+60+70+70+70+24)/9 = 53.56 pounds
Median: 60 pounds
Mode: There is no mode because no weight appears more than once.
The best measure of central tendency for this data is the median because it is not affected by outliers in the data (if one dog weighed significantly more or less than the others) and it gives a value that is representative of the "middle" weight.
To find the weight of the 10th dog needed to make the average weight 250 pounds, we can use the formula:
(new average weight) = (sum of all weights + weight of 10th dog) / 10
250 = (sum of all weights + weight of 10th dog) / 10
sum of all weights + weight of 10th dog = 2500
Using the average weights listed above, we can find the sum of all weights:
65+45+35+55+60+70+70+70+24 = 504
So, we can substitute this into the equation:
504 + weight of 10th dog = 2500
weight of 10th dog = 1996 pounds
This number is obviously unrealistic and impossible for a dog to weigh, which means it is not possible to have a 10th dog that would make the average weight 250 pounds.