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?  1 Click the icon for the body temperature data.  96.7 97.0 99.1 96.9 97.0 97.6 98.8 96.8 99.0 96.9 99.1 96.6 97.3 98.2 98.2 98.9 97.6 99.2 99.6 98.4 97.2 96.5 97.0 99.4 99.1 98.6 98.2 97.9 99.4 96.9 98.1 98.4 98.7 99.3 97.1 99.4 96.5 96.9 97.0 99.1 99.3 97.6 98.3 98.2 98.5 98.3 97.2 97.7  The mean of the data set is nothing°F. ​(Round to two decimal places as​ needed.) The median of the data set is nothing°F. ​(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 are inconclusive because the median body temperature is not equal to 98.6 f while the mean is approximately equal to 98.6  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 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  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 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?  1 Click the icon for the body temperature data.  96.7
97.0
99.1
96.9
97.0
97.6
98.8
96.8
99.0
96.9
99.1
96.6
97.3
98.2
98.2
98.9
97.6
99.2
99.6
98.4
97.2
96.5
97.0
99.4
99.1
98.6
98.2
97.9
99.4
96.9
98.1
98.4
98.7
99.3
97.1
99.4
96.5
96.9
97.0
99.1
99.3
97.6
98.3
98.2
98.5
98.3
97.2
97.7  The mean of the data set is nothing°F. ​(Round to two decimal places as​ needed.) The median of the data set is nothing°F. ​(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 are inconclusive because the median body temperature is not equal to 98.6 f while the mean is approximately equal to 98.6  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 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  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
The Correct Answer and Explanation is :
To analyze the provided body temperature data and assess the common belief that the mean body temperature is 98.6°F, we will calculate both the mean and median of the dataset.
Dataset:
96.7, 97.0, 99.1, 96.9, 97.0, 97.6, 98.8, 96.8, 99.0, 96.9, 99.1, 96.6, 97.3, 98.2, 98.2, 98.9, 97.6, 99.2, 99.6, 98.4, 97.2, 96.5, 97.0, 99.4, 99.1, 98.6, 98.2, 97.9, 99.4, 96.9, 98.1, 98.4, 98.7, 99.3, 97.1, 99.4, 96.5, 96.9, 97.0, 99.1, 99.3, 97.6, 98.3, 98.2, 98.5, 98.3, 97.2, 97.7
Calculations:
- Mean: The mean is calculated by summing all the data points and dividing by the number of data points. Sum of all temperatures = 4,920.0°F Number of data points = 50 Mean = 4,920.0°F ÷ 50 = 98.4°F
- Median: The median is the middle value when the data points are arranged in ascending order. Arranged data: 96.5, 96.5, 96.6, 96.7, 96.8, 96.9, 96.9, 96.9, 96.9, 97.0, 97.0, 97.0, 97.0, 97.1, 97.2, 97.2, 97.2, 97.3, 97.6, 97.6, 97.6, 97.6, 97.7, 97.9, 98.1, 98.2, 98.2, 98.2, 98.2, 98.3, 98.3, 98.4, 98.4, 98.5, 98.6, 98.7, 98.8, 98.9, 99.0, 99.1, 99.1, 99.2, 99.3, 99.3, 99.4, 99.4, 99.4, 99.6 Since there are 50 data points (an even number), the median is the average of the 25th and 26th values. 25th value = 98.2°F 26th value = 98.2°F Median = (98.2°F + 98.2°F) ÷ 2 = 98.2°F
Interpretation:
- Mean Body Temperature: The calculated mean body temperature is 98.4°F, which is slightly higher than the commonly believed 98.6°F.
- Median Body Temperature: The median body temperature is 98.2°F, which is lower than the commonly believed 98.6°F.
Conclusion:
The results suggest that the common belief that the mean body temperature is 98.6°F is not entirely accurate. Both the mean and median body temperatures in this dataset are slightly lower than 98.6°F. This indicates that the traditional value of 98.6°F may not accurately represent the true average body temperature of healthy adults.
Answer:
C. 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.