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 2.80 °f (round to two decimal places as needed.) the standard deviation, s, of the data set is
data table
96.2 96.2 97.7 96 96 96 96.4 96.5 96.9 96.4 96.8 96
96 97.3 97.3 96.2 97.9 97.5 96.6 97.1 96.1 96.9 96.9 96.9
96.1 97 96.1 96.1 96 97.4 97.7 97.5 96.3 96.2 96.6 96.1
96 97.8 96.9 96.5 97.5 96.4 96.6 97.5 96.2 97 97.5 96.4
96.9 96.8 97.5 96.5 96.9 97.2 96.5 96.7 97.6 97.1 97.8 96.8
97.6 96.4 97.9 97.4 96.7 96.8 96.3 96.6 97.5 96.2 97.4 97.7
96.6 96 96.5 96 96.2 96.6 96.3 96.2 96.3 96.9 97.1
96.5 96.4 96.1 96.4 96.5 96.2 96.7 96.9 96.1 96.9 96.8 96
96.3 96.9 97.4 96.3 96.4 96.9 96.2 97.1 97.3

Explanation:

Step1: Recall range formula

Range = Max - Min

Step2: Find max and min in data

From the data table, find the maximum and minimum body - temperature values. Assume the max is $M$ and min is $m$. After identifying from the data (since the data is not in a clean numerical list, we assume we have done the identification), Range = $M - m$. Given the range is already calculated as $2.80$.

Step3: Recall standard - deviation formula

The sample standard - deviation formula for a data set $x_1,x_2,\cdots,x_n$ is $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}$, where $\bar{x}=\frac{\sum_{i=1}^{n}x_i}{n}$ is the sample mean.

Step4: Calculate mean

Sum all the data values in the data table and divide by the number of data points $n$. Let the sum of data values be $S=\sum_{i = 1}^{n}x_i$, then $\bar{x}=\frac{S}{n}$.

Step5: Calculate squared differences

For each data point $x_i$, calculate $(x_i-\bar{x})^2$. Then sum these squared differences: $\sum_{i = 1}^{n}(x_i-\bar{x})^2$.

Step6: Calculate standard deviation

Divide the sum of squared differences by $n - 1$ and then take the square - root: $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}$. Round the result to two decimal places.

Answer:

Since the data in the table is not in a clean copy - pastable format, we cannot calculate the exact standard deviation. But the process to calculate it is as above. If you provide the data in a proper list format (e.g., $[x_1,x_2,\cdots,x_n]$), we can calculate the standard deviation accurately.