Measurement Scales

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a) Describe the data scales that are best suited for presentation in a pie chart. How effective are the pie charts that often accompany a newspaper article in explaining the statistics being used in the article? Using any data real or fictional, develop a pie chart and interpret the results.
b) Does all data have a mean, median, or mode? Why or why not? When is the mean the best measure of central tendency? When is the median the best measure of central tendency?

Background information:
Data scales are classified as (a) nominal, (b) ordinal, (c) interval or (d) ratio
Nominal data scale allows for only qualitative classification. That is, they can be measured only in terms of whether the individual items belong to some distinctively different categories, but we cannot quantify or even rank order those categories. Typical examples of nominal variables are gender (Male, Female), race, color, city, etc.
Ordinal data scale allows us to rank order the items we measure in terms of which has less and which has more of the quality represented by the variable, but still they do not allow us to say "how much more." A typical example of an ordinal variable is the socioeconomic status of families. For example, we know that upper-middle is higher than middle but we cannot say that it is, for example, 28% higher.
Interval data scale allows us not only to rank order the items that are measured, but also to quantify and compare the sizes of differences between them. Example: temperature, (degrees Fahrenheit or Celsius) is an interval scale. We can say that a temperature of 40 degrees is higher than a temperature of 30 degrees, and that an increase from 20 to 40 degrees is twice as much as an increase from 30 to 40 degrees.
Ratio data scale is very similar to interval variables; in addition to all the properties of interval variables, they feature an identifiable absolute zero point, thus they allow for statements such as x is two times more than y. Typical examples of ratio scales are measures of time or space.

a) Describe the data scales that are best suited for presentation in a pie chart. How ...