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 standard deviation is an extremely important concept introduced in Chapter 3. Using the sample data from Exercise 1 “Birth Weights,” part of the calculation of the standard deviation is shown in the expression below. Evaluate this expression. (Fortunately, calculators and software are designed to automatically execute such expressions, so our future work with standard deviations will not be burdened with cumbersome calculations.)

\(\frac{{{{\left( {3660 - 3162.5} \right)}^2}}}{7}\)

Short answer

The value of the expression is equal to 27343.75.

Step-by-step solution

 Step 1: Given information

The weights (in grams) are considered for 8 newborn babies. The sample standard deviation has the given expression as a part of its calculation

Evaluation of the expression

The value of the given expression is computed as shown below:

\(\begin{array}{c}\frac{{{{\left( {3660 - 3162.5} \right)}^2}}}{7} = \frac{{191406.3}}{7}\\ = 27343.75\end{array}\)

Thus, the value of the expression is equal to 27343.75.