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A histogram with five bars of varying heights shows dog weights in pounds with the number of dogs. The horizontal axis shows Dog Weight in Pounds ranging from 20 to 40 in increments of 4. The vertical axis shows Number of Dogs ranging from 0 to 12 in increments of 2. The data reads as follows: Dog weight from 20 to 24 pounds; number of dogs: 11. Dog weight from 24 to 28 pounds; number of dogs: 11. Dog weight from 28 to 32 pounds; number of dogs: 2. Dog weight from 32 to 36 pounds; number of dogs: 3. Dog weight from 36 to 40 pounds; number of dogs: 3.

The histogram shows the data from a pet show. If you have a circle graph of the same dataset, which of the following would be true?

(1 point)
Responses

There will be five equal sections on the circle.
There will be five equal sections on the circle.

The largest section will be the 28–32 pound interval.
The largest section will be the 28–32 pound interval.

The smallest section will be the 28–32 pound interval.
The smallest section will be the 28–32 pound interval.

The percentages for all five sections will be the same.

1 answer

To analyze the histogram data provided for dog weights:

  • Dog weight from 20 to 24 pounds: 11 dogs
  • Dog weight from 24 to 28 pounds: 11 dogs
  • Dog weight from 28 to 32 pounds: 2 dogs
  • Dog weight from 32 to 36 pounds: 3 dogs
  • Dog weight from 36 to 40 pounds: 3 dogs

Now, let's total the number of dogs:

Total number of dogs = 11 + 11 + 2 + 3 + 3 = 40 dogs.

Now we can determine the percentage of dogs in each weight interval for the circle graph:

  1. Dog weight 20–24 pounds: (11/40) * 100 = 27.5%
  2. Dog weight 24–28 pounds: (11/40) * 100 = 27.5%
  3. Dog weight 28–32 pounds: (2/40) * 100 = 5%
  4. Dog weight 32–36 pounds: (3/40) * 100 = 7.5%
  5. Dog weight 36–40 pounds: (3/40) * 100 = 7.5%

From this analysis:

  • The largest sections will be for 20–24 pounds and 24–28 pounds, both at 27.5%.
  • The smallest section will be for the 28–32 pounds with only 5%.
  • The percentages for all five sections are not the same and vary based on the number of dogs in each weight category.

Thus, the correct response from the options would be:

The smallest section will be the 28–32 pound interval.