Questions: 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. The range of the data set is degrees F. (Round to two decimal places as needed.) Data table 98.5 98.7 97.6 97.9 99 98.4 97.9 98.6 98.3 98.6 98.2 99.1 98.7 96.8 96.8 98.5 98 97.9 98.5 97.6 97.6 98.5 98.9 96.8 98.2 97.9 99.3 98.5 99.9 97.6 97.3 97.1 98 99.9 98.9 99.3 98.3 97.8 98.4 98.4 97 98.4 98.2 97.9 97.5 97.5 97.8 98 98.3 99 98.3 99.3 96.6 97.8 97.9 97.1 97.8 96.7 97.8 98.4 97.5 98.1 97.8 97.9 97.7 98.1 98.8 98.9 97.9 98.4 97.1 97.6 99.3 98.8 98.9 98.5 98.6 98.8 98.8 99 99 99.4 98.3 97.4 98.9 98.2 98.6 98.6 98.9 97.9 98.8 97.1 98.3 99.1 98.8 97.8 98.4 99 97.5 98.5 98.6 97.9 98.4 97.3 97.8 96.8

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. The range of the data set is degrees F. (Round to two decimal places as needed.) Data table 98.5 98.7 97.6 97.9 99 98.4 97.9 98.6 98.3 98.6 98.2 99.1 98.7 96.8 96.8 98.5 98 97.9 98.5 97.6 97.6 98.5 98.9 96.8 98.2 97.9 99.3 98.5 99.9 97.6 97.3 97.1 98 99.9 98.9 99.3 98.3 97.8 98.4 98.4 97 98.4 98.2 97.9 97.5 97.5 97.8 98 98.3 99 98.3 99.3 96.6 97.8 97.9 97.1 97.8 96.7 97.8 98.4 97.5 98.1 97.8 97.9 97.7 98.1 98.8 98.9 97.9 98.4 97.1 97.6 99.3 98.8 98.9 98.5 98.6 98.8 98.8 99 99 99.4 98.3 97.4 98.9 98.2 98.6 98.6 98.9 97.9 98.8 97.1 98.3 99.1 98.8 97.8 98.4 99 97.5 98.5 98.6 97.9 98.4 97.3 97.8 96.8
Transcript text: 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. The range of the data set is $\square$ ${ }^{\circ} \mathrm{F}$. (Round to two decimal places as needed.) Data table \[ \begin{array}{llllllllllllll} 98.5 & 98.7 & 97.6 & 97.9 & 99 & 98.4 & 97.9 & 98.6 & 98.3 & 98.6 & 98.2 & 99.1 \\ 98.7 & 96.8 & 96.8 & 98.5 & 98 & 97.9 & 98.5 & 97.6 & 97.6 & 98.5 & 98.9 & 96.8 \\ 98.2 & 97.9 & 99.3 & 98.5 & 99.9 & 97.6 & 97.3 & 97.1 & 98 & 99.9 & 98.9 & 99.3 \\ 98.3 & 97.8 & 98.4 & 98.4 & 97 & 98.4 & 98.2 & 97.9 & 97.5 & 97.5 & 97.8 & 98 \\ 98.3 & 99 & 98.3 & 99.3 & 96.6 & 97.8 & 97.9 & 97.1 & 97.8 & 96.7 & 97.8 & 98.4 \\ 97.5 & 98.1 & 97.8 & 97.9 & 97.7 & 98.1 & 98.8 & 98.9 & 97.9 & 98.4 & 97.1 & 97.6 \\ 99.3 & 98.8 & 98.9 & 98.5 & 98.6 & 98.8 & 98.8 & 99 & 99 & 99.4 & 98.3 & 97.4 \\ 98.9 & 98.2 & 98.6 & 98.6 & 98.9 & 97.9 & 98.8 & 97.1 & 98.3 & 99.1 & 98.8 & 97.8 \\ 98.4 & 99 & 97.5 & 98.5 & 98.6 & 97.9 & 98.4 & 97.3 & 97.8 & 96.8 & & & \end{array} \]
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Solution

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Solution Steps

Step 1: Calculate the Range

The range of the data set is calculated as follows:

\[ \text{Range} = \max(x_i) - \min(x_i) = 99.9 - 96.6 = 3.30 \, ^\circ \text{F} \]

Step 2: Calculate the Mean

The mean \( \mu \) of the data set is given by:

\[ \mu = \frac{\sum x_i}{n} = \frac{10409.3}{106} \approx 98.2 \]

Step 3: Calculate the Variance

The variance \( \sigma^2 \) is calculated using the formula:

\[ \sigma^2 = \frac{\sum (x_i - \mu)^2}{n-1} = 0.49 \]

Step 4: Calculate the Standard Deviation

The standard deviation \( \sigma \) is the square root of the variance:

\[ \sigma = \sqrt{0.49} = 0.7 \]

Final Answer

  • The range of the data set is \( 3.30 \, ^\circ \text{F} \).
  • The variance of the data set is \( 0.49 \).
  • The standard deviation of the data set is \( 0.70 \).

Thus, the final answers are: \[ \boxed{\text{Range} = 3.30 \, ^\circ \text{F}, \, \text{Variance} = 0.49, \, \text{Standard Deviation} = 0.70} \]

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