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 One way to get a very rough approximation of the value of a standard deviation of sample data is to find the range, then divide it by 4. The range is the difference between the highest sample value and the lowest sample value. In using this approach, what value is obtained from the sample data listed in Exercise 1 “Birth Weights”?

Short answer

For the sample of weights of eight babies (in grams), the approximate value of the sample standard deviation is equal to 575 grams.

Step-by-step solution

Given information

A sample of weights of babies (in grams) is given. The total number of babies is eight. For this sample, the standard deviation is to be computed.

Determining the standard deviation

The sample standard deviation can be approximated using therule of range.

Range: Subtracting the minimum value of the dataset from its maximum value gives the range of the dataset.

The rule of range states that thestandard deviationof the data is nearly one-fourth of the range. That is

\({\rm{Standard}}\;{\rm{Deviation}} = \frac{{{\rm{Maximum}}\;{\rm{value}} - {\rm{Minimum}}\;{\rm{value}}}}{4}\)

The range for the given data of weights is equal to 2300 grams, as shown below:

\(\begin{array}{c}{\rm{Range}} = 4000 - 1700\\ = 2300\end{array}\)

The rough estimate of the standard deviation for the weights is calculated as:

\(\begin{array}{c}{\rm{Standard}}\;{\rm{Deviation}} = \frac{{4000 - 1700}}{4}\\ = \frac{{2300}}{4}\\ = 575\end{array}\)

Thus, the rough estimate of the standard deviation for the weights is equal to 575 grams.