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 3.40 °f (round to two decimal places as needed.) the standard deviation, s, of the data set is °f (round to two decimal places as needed.) data table 98.6 98.5 97.7 97.9 98.6 98.2 98.6 98.9 98.2 98.2 98.5 98.6 98.6 97.4 96.6 99.3 97.5 97.9 98.7 98.1 98.3 98.3 98.2 97.4 98.5 97.7 98.5 98.7 99.7 97.6 97.4 97.6 98.5 99.5 99 99.9 98.5 97.8 98.8 98.7 96.7 98.6 98.7 98.6 98.2 97.9 98 98.3 98.9 98.7 98.3 99.2 96.5 97.7 97.7 97.4 97.3 97.2 97.5 98.3 96.9 97.6 97.3 97.8 98.2 98.9 98.8 98.2 97.4 97.6 96.7 97 99 98.7 98.7 98 98.9 98.4 98.7 98.9 98.6 99.3 98.9 97.5 98.9 98.4 98.2 98.2 98.6 98.7 98.8 96.8 97.6 98.6 98.6 98.1 98.1 99.6 97.7 98.3 98 97.8 98.2 97.5 97.9 97.4

Explanation:

Step1: Recall the formula for standard - deviation

The formula for the sample standard deviation $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$, where $x_{i}$ are the data points, $\bar{x}$ is the sample mean, and $n$ is the number of data points. First, find the mean $\bar{x}$.
Let the data set be $x_1,x_2,\cdots,x_n$. The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$.
Counting the number of data points $n = 80$.
$\sum_{i=1}^{80}x_{i}=98.6 + 98.5+97.7+\cdots+97.4=7847.9$
$\bar{x}=\frac{7847.9}{80}=98.09875$

Step2: Calculate $(x_{i}-\bar{x})^{2}$ for each data - point

For example, if $x_1 = 98.6$, then $(x_1-\bar{x})^{2}=(98.6 - 98.09875)^{2}=(0.50125)^{2}=0.2512515625$
Do this for all 80 data points and sum them up: $\sum_{i = 1}^{80}(x_{i}-\bar{x})^{2}=48.79875$

Step3: Calculate the variance

The sample variance $s^{2}=\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}=\frac{48.79875}{79}\approx0.6177$

Step4: Calculate the standard deviation

The sample standard deviation $s=\sqrt{s^{2}}=\sqrt{0.6177}\approx0.79$

Answer:

$0.79$