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Refer to the data set of body temperatures in degrees Fahrenheit given in the accompanying table and use software or a calculator to find the mean and median.

Do the results support or contradict the common belief that the mean body temperature is 98.6°F?

**Body Temperatures (°F)**:
- 99.5, 97.5, 96.5, 98.4, 98.7, 97.5, 97.5, 99.3, 98.3, 96.6
- 98.2, 98.2, 97.9, 98.2, 99.4, 98.1, 98.5, 98.7, 98.7, 97.5
- 97.3, 98.8, 99.2, 99.6, 98.4, 97.1, 98.2, 96.9, 97.8, 98.9
- 98.6, 97.1, 99.4, 99.0, 96.8, 99.4, 99.0, 98.5, 97.5, 98.8
- 97.5, 96.6, 97.6, 99.5, 97.6, 97.5, 97.4, 98.2

The mean of the dataset is ____. (Round to two decimal places as needed.)

The median of the dataset is ____. (Type an integer or a decimal. Do not round.)

Do the results support or contradict the common belief that the mean body temperature is 98.6°F?

A. The results contradict the belief that the mean body temperature is 98.6°F because both the mean and the median are less than 98.6°F.
B. The results are inconclusive because the mean body temperature is not equal to 98.6°F while the median is approximately equal to 98.6°F.
C. The results are inconclusive because the median body temperature is not equal to 98.6°F while the mean is approximately equal to 98.6°F.
D. The results support the belief that the mean body temperature is 98.6°F because both the mean and the median are equal to 98.6°F.

Answer :

The mean body temperature is approximately 90.91°F and the median is 97.9°F. The results contradict the common belief of a mean body temperature of 98.6°F.

The mean and median of a data set can provide insights into its central tendency. To find the mean, you would sum up all the values in the data set and divide by the total number of values. In this case, summing up all the given body temperatures, you get a sum of 3898.9. Dividing this by 43 (the total number of temperatures), you find that the mean body temperature is approximately 90.91°F.

For the median, you would arrange the data set in ascending order and find the middle value. Since there are 43 data points, the middle value is the 22nd value. When the data set is arranged in ascending order, the 22nd value is 97.9°F. Therefore, the median body temperature is 97.9°F.

Based on these calculations, the mean and median are both less than 98.6°F. Therefore, the results contradict the common belief that the mean body temperature is 98.6°F. The answer is option A: The results contradict the belief that the mean body temperature is 98.6°F because both the mean and the median are less than 98.6°F.

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