Question

For Chapter 2 through Chapter 14, the Cumulative Review Exercises include topics from preceding chapters. For this chapter, we present a few calculator warm-up exercises, with expressions similar to those found throughout this book. Use your calculator to find the indicated values.

Standard Deviation The given expression is used to compute the standard deviation of three randomly selected body temperatures. Perform the calculation and round the result to two decimal places.

\(\sqrt {\frac{{{{\left( {98.4 - 98.6} \right)}^2} + {{\left( {98.6 - 98.6} \right)}^2} + {{\left( {98.8 - 98.6} \right)}^2}}}{{3 - 1}}} \)

Short answer

For the given sample of body temperatures with a sample size equal to 3, the calculated standard deviation using the given expression is equal to 0.20.

Step-by-step solution

Given information

A random sample of three body temperatures is considered.

An expression is provided to calculate the sample standard deviation.

Standard deviation of a sample

The standard deviation of a sample of n observations is obtained using the following expression:

\({\rm{Standard}}\;{\rm{deviation}} = \sqrt {\frac{{\sum\limits_{i = 1}^n {{{\left( {{x_i} - \bar x} \right)}^2}} }}{{n - 1}}} \)

Here,

\({x_i}\)denotes the ith observation of the sample.

\(\bar x\)denotes the sample mean.

It gives an idea of how far each value of the dataset is spread from the average value.

Calculations involved

Using the given expression, the standard deviation is calculated as shown below:

\(\begin{array}{c}\sqrt {\frac{{{{\left( {98.4 - 98.6} \right)}^2} + {{\left( {98.6 - 98.6} \right)}^2} + {{\left( {98.8 - 98.6} \right)}^2}}}{{3 - 1}}} = \sqrt {\frac{{{{\left( { - 0.20} \right)}^2} + {{\left( {0.00} \right)}^2} + {{\left( {0.20} \right)}^2}}}{{3 - 1}}} \\ = \sqrt {\frac{{0.04 + 0 + 0.04}}{2}} \\ = \sqrt {0.04} \\ = 0.20\end{array}\)

Thus, the standard deviation is 0.20.