Questions: Body temperature (in degrees Fahrenheit) of randomly selected normal and healthy adults are shown below. Compute the mean, median, and mode of the data set 98.3, 98.6, 98.4, 98.2, 98.1, 98.1, 98.5, 98.0, 98.1, 98.8, The mean is degrees F. (Round to the nearest hundredth as needed.) The median is degrees F. (Round to the nearest hundredth as needed.) What is/are the mode(s)? Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The mode(s) is/are degrees F. (Use a comma to separate answers as needed.) B. There is no mode.

Solution Steps

The mean \( \mu \) of the body temperature data is calculated using the formula:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} \]

where \( N \) is the number of data points and \( x_i \) are the individual data values. For the given data:

\[ \sum_{i=1}^{10} x_i = 98.3 + 98.6 + 98.4 + 98.2 + 98.1 + 98.1 + 98.5 + 98.0 + 98.1 + 98.8 = 983.1 \]

Thus, the mean is:

\[ \mu = \frac{983.1}{10} = 98.31 \]

To find the median, we first sort the data:

\[ \text{Sorted data} = [98.0, 98.1, 98.1, 98.1, 98.2, 98.3, 98.4, 98.5, 98.6, 98.8] \]

Since there are \( N = 10 \) data points (an even number), the median \( Q \) is calculated as the average of the 5th and 6th values:

\[ \text{Rank} = Q \times (N + 1) = 0.5 \times (10 + 1) = 5.5 \]

Thus, we find:

\[ Q = \frac{X_{\text{lower}} + X_{\text{upper}}}{2} = \frac{98.2 + 98.3}{2} = 98.25 \]

The mode is the value that appears most frequently in the dataset. By counting the occurrences of each value, we find:

• \( 98.1 \) appears 3 times,
• All other values appear less frequently.

Thus, the mode(s) is/are:

\[ \text{Mode} = 98.1 \]

Final Answer