Question

Which of the five measures of center (the mean, the median, the trimmed mean, the weighted mean, and the mode) can be calculated for quantitative data only.

Answer 1

Quantitative data is defined as information that gives measurement or it can be written down in numbers.

Each of these five measures of center 1) the mean, 2) the median, 3)the trimmed mean, 4) the weighted mean, and 5) the mode can be measured and written down in number. Thus, they are all quantitative data. 

Answer 2

In Chapter 2 we discussed how to summarize data using different methods and to display data using graphs. Graphs are one important component of statistics; however it is also important to numerically describe the main characteristics of a data set. The numerical summary measures, such as the ones that identify the center and spread of a distribution, identify many important features of a distribution. For example, the techniques learned in Chapter 2 can help us graph data on family incomes. However, if we want to know the income of a “typical” family (given by the center of the distribution), the spread of the distribution of incomes, or the relative position of a family with a particular income, the numerical summary measures can provide more detailed information (see Figure 3.1). The measures that we discuss in this chapter include measures of (1) central tendency, (2) dispersion (or spread), and (3) position.