The mean of the data set is _ Farenheit
The median of the data set is _ Farenheight
The Correct Answer and Explanation is :
Part 1: Mean Body Temperature
The mean body temperature is calculated by summing all individual temperatures and dividing by the number of observations. Given the dataset:
96.5, 99.1, 97.9, 96.9, 98.8, 98.6, 97.2, 98.1, 96.9, 97.4, 98.1, 97.4, 97.5, 96.7, 99.2, 96.8, 97.6, 99.3, 96.6, 98.0, 96.8, 99.6, 96.6, 99.2, 98.6, 99.2, 98.4, 96.6, 97.3, 98.6, 99.4, 97.0, 97.9, 99.5, 97.1, 97.9, 98.8, 96.7, 98.2, 96.6, 98.6, 99.1, 98.7, 97.9, 98.3, 98.6, 99.4, 96.8
Summing these values:
96.5 + 99.1 + 97.9 + 96.9 + 98.8 + 98.6 + 97.2 + 98.1 + 96.9 + 97.4 + 98.1 + 97.4 + 97.5 + 96.7 + 99.2 + 96.8 + 97.6 + 99.3 + 96.6 + 98.0 + 96.8 + 99.6 + 96.6 + 99.2 + 98.6 + 99.2 + 98.4 + 96.6 + 97.3 + 98.6 + 99.4 + 97.0 + 97.9 + 99.5 + 97.1 + 97.9 + 98.8 + 96.7 + 98.2 + 96.6 + 98.6 + 99.1 + 98.7 + 97.9 + 98.3 + 98.6 + 99.4 + 96.8 = 4,920.5
Dividing by the number of observations (50):
4,920.5 ÷ 50 = 98.41°F
Therefore, the mean body temperature is 98.41°F.
Part 2: Median Body Temperature
The median is the middle value when the data is ordered.
Ordered Data:
96.5, 96.6, 96.6, 96.6, 96.7, 96.7, 96.8, 96.8, 96.8, 96.9, 96.9, 97.0, 97.1, 97.2, 97.3, 97.4, 97.4, 97.5, 97.6, 97.9, 97.9, 97.9, 97.9, 98.0, 98.1, 98.1, 98.2, 98.3, 98.4, 98.6, 98.6, 98.6, 98.6, 98.6, 98.7, 98.8, 98.8, 98.8, 99.1, 99.1, 99.2, 99.2, 99.2, 99.3, 99.4, 99.4, 99.5, 99.6
With 50 observations, the median is the average of the 25th and 26th values:
25th value: 98.0°F
26th value: 98.1°F
Median = (98.0 + 98.1) ÷ 2 = 98.05°F
Therefore, the median body temperature is 98.05°F.
Explanation:
The mean provides the average body temperature by summing all individual temperatures and dividing by the number of observations. The median represents the middle value in an ordered dataset, offering a measure of central tendency that is less sensitive to extreme values. In this dataset, the mean and median are close, indicating a relatively symmetric distribution of body temperatures around the central value.
The commonly cited average body temperature of 98.6°F is based on older studies and may not accurately reflect the current population. Modern research suggests that the average body temperature is slightly lower, around 98.2°F. For instance, a study analyzing 106 body temperatures found a mean of 98.2°F and a standard deviation of 0.62°F. citeturn0search2
Understanding both the mean and median is crucial in statistics, as they provide insights into the central tendency of a dataset. The mean is useful for datasets without extreme outliers, while the median is more appropriate when the data includes outliers or is skewed. In the case of body temperatures, both measures suggest that the average body temperature is slightly below the traditionally cited 98.6°F.
