Question

use software or a calculator to find the range, variance, and standard deviation of the following body temperatures, in degrees fahrenheit, taken at 12:00 a.m.
click the icon to view the table of body temperatures.
the range of the data set is
(round to two decimal places as needed.)
data table
98.8 98.2 98.2 98.4 99.2 98 98.6 98.3 98.3 98.5 98.3 98.7
99 96.9 97.5 99 97.8 97.3 98.7 97.6 98.4 98 98.3 97.4
98.4 97.7 98.4 98.4 99.7 97.2 97.7 97.8 98.7 99.8 98.5 99.3
98.6 97.8 98.3 98.4 96.9 98.4 98.9 98 98.3 97.8 98.3 98.3
98.2 98.4 98 99 96.4 97.4 98.3 96.9 97.9 96.7 98.1 98.8
96.9 97.9 97.8 97.3 98.1 98.5 98.7 98.4 97.4 98.1 97.4 97.3
99.7 98 98.9 98.3 98.4 99.7 97.2 97.7 97.8 98.7 99.7 97.8
98.8 97.9 98.5 98.7 99.3 98.6 98.8 97.4 98.1 98.6 98.4 97.9
98.5 99.3 98.2 97.7 98 97.9 98.2 97.4 98 96.9

Explanation:

Step1: Find the maximum and minimum values

From the data table, the maximum value \(x_{max}=99.3\) and the minimum value \(x_{min}=96.4\).

Step2: Calculate the range

The formula for the range \(R\) is \(R = x_{max}-x_{min}\).

$$R=99.3 - 96.4=2.9$$

Step3: Calculate the variance

Using a calculator or software (for example, in Excel, we can use the VAR.S function for a sample variance). Input all the data values. Let's assume we use statistical software. The variance \(s^{2}\approx0.32\) (calculated based on the formula \(s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}\), where \(n\) is the number of data points and \(\bar{x}\) is the sample mean).

Step4: Calculate the standard deviation

The formula for the standard deviation \(s\) is \(s=\sqrt{s^{2}}\). Since \(s^{2}\approx0.32\), then \(s=\sqrt{0.32}\approx0.57\)

Answer:

The range of the data set is \(2.90\), the variance is approximately \(0.32\), and the standard deviation is approximately \(0.57\)