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.

Birth Weights Listed below are the weights (grams) of newborn babies from Albany Medical Center Hospital. What value is obtained when those weights are added and the total is divided by the number of weights? (This result, called the mean, is discussed in Chapter 3.) What is notable about these values, and what does it tell us about how the weights were measured?

3600 1700 4000 3900 3100 3800 2200 3000

Short answer

The total sum of the weights of the babies divided by the total number of babies is equal to 3162.5 grams.

All the given values of the weights end with a 00. Thus, it indicates that these weights were rounded to the nearest 100 grams at the time of measurement.

Step-by-step solution

Given information

The weights (in grams) of eight newborn babies born at the Albany Medical Center Hospital are provided. The values are summed up and then divided by the number of babies.

Arithmetic mean of numerical data

Themean (average) value for a given set of numerical values commonly represents the data as most observations fall around that value.

When all the given values are added and then divided by the total count of values, the arithmetic mean is obtained.

  Determining the mean value

Thesumof the weights given is calculated as shown below:

\(\begin{array}{c}{\rm{Sum}} = 3600 + 1700 + 4000 + 3900 + 3100 + 3800 + 2200 + 3000\\ = 25300\end{array}\)

Thus, thesum of the weights is equal to25,300 grams.

The total number of weights given is equal to 8.

The mean valueis calculated as follows:

\(\begin{array}{c}{\rm{Mean}} = \frac{{3600 + 1700 + 4000 + 3900 + 3100 + 3800 + 2200 + 3000}}{8}\\ = \frac{{25300}}{8}\\ = 3162.5\end{array}\)

Thus, the mean valueis obtained to be equal to 3162.5 grams.

Observing the given values

By observing the given values of weights, it can be seen that all of them have00 at the end.

To ease calculations, numerical data is oftenrounded off to the nearest 100 or 1000, according to the units it is measured in.

Thus, at the time of measurement, the values wererounded to the nearest 100 grams.