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Question 7 • Mathematics III

The histograms show the ages of dogs at four different shelters. For which set of data is the mean most likely greater than the median?

Answer

Image with description A bar graph represents the ages of dogs at five different shelters. The horizontal axis lists 0-1 to 8-9 and is labeled as age. The vertical axis lists 0 to 2 and is labeled as the number of dogs. There are 5 bars on the graph. The first bar represents the 0-1 age group of dogs and shows shelter for 2 dogs, the second bar represents the 2-3 age group of dogs and shows shelter for 1 dog, the third bar represents the 4-5 age group of dogs and shows shelter for 2 dogs, the fourth bar represents the 6-7 age group of dogs and shows shelter for 1 dog, and the fifth bar represents the 8-9 age group of dogs and shows shelter for 2 dogs.

Image with description A bar graph represents the ages of dogs at five different shelters. The horizontal axis lists 0-1 to 8-9 and is labeled as age. The vertical axis lists 0 to 4 and is labeled as the number of dogs. There are 5 bars on the graph. The first bar represents the 0-1 age group of dogs and shows shelter for 0 dogs, the second bar represents the 2-3 age group of dogs and shows shelter for 1 dog, the third bar represents the 4-5 age group of dogs and shows shelter for 2 dogs, the fourth bar represents the 6-7 age group of dogs and shows shelter for 4 dogs, and the fifth bar represents the 8-9 age group of dogs and shows shelter for 1 dog.

Image with description A bar graph represents the ages of dogs at five different shelters. The horizontal axis lists 0-1 to 8-9 and is labeled as age. The vertical axis lists 0 to 4 and is labeled as the number of dogs. There are 5 bars on the graph. The first bar represents the 0-1 age group of dogs and shows shelter for 1 dog, the second bar represents the 2-3 age group of dogs and shows shelter for 4 dogs, the third bar represents the 4-5 age group of dogs and shows shelter for 2 dogs, the fourth bar represents the 6-7 age group of dogs and shows shelter for 0 dogs, and the fifth bar represents the 8-9 age group of dogs and shows shelter for 1 dog.

Image with description A bar graph represents the ages of dogs at five different shelters. The horizontal axis lists 0-1 to 8-9 and is labeled as age. The vertical axis lists 0 to 4 and is labeled as the number of dogs. There are 5 bars on the graph. The first bar represents the 0-1 age group of dogs and shows shelter for 0 dogs, the second bar represents the 2-3 age group of dogs and shows shelter for 3 dogs, the third bar represents the 4-5 age group of dogs and shows shelter for 4 dogs, the fourth bar represents the 6-7 age group of dogs and shows shelter for 3 dogs, and the fifth bar represents the 8-9 age group of dogs and shows shelter for 0 dogs.

Explanation

In choice C, most dogs are in the younger 2–3 age group, while a dog in the 8–9 group creates a tail toward the older ages. Using the age-group midpoints, the mean is about (0.5 + 4×2.5 + 2×4.5 + 8.5) ÷ 8 = 3.25, while the median is about 2.5. Thus, the mean is greater than the median for choice C.

AI-written and checked against the verified answer.

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