This chapter has provided an introduction to descriptive statistics. Now that you have read this chapter, you should understand the following concepts and techniques:
- Descriptive statistics are used to summarize and describe a group of numbers.
- A variable is a characteristic that can take on any number of different values. Values can be numbers or categories and a given individual's value on a particular variable is that individual's score.
- There are two kinds of numeric variables: equal-interval variables (for which the values are numbers that stand for approximately equal amounts of what is being measured) and rank-order variables (for which the values are ranks). In addition, some variables are nominal variables (for which the values are categories). The kind of variable used most often by social and behavioral scientists is the equal-internal variable.
- A frequency table is a table that shows how many times each value was used for a particular variable, along with the percentage of scores of each value. A grouped frequency table records the frequency of a range of scores within certain equally sized intervals rather than the frequency of individual values.
- A histogram depicts the information from a frequency table as a bar graph. A frequency polygon depicts the same information by plotting a point to show the frequency of each value or range of values and then joining these points with a line.
- The shape of a frequency distribution can be characterized as unimodal (having one peak), bimodal (having two peaks), multimodal (having two or more peaks). If a frequency distribution has no peaks-in other words, if the values all have about the same frequency-is can be described as rectangular.
- A frequency distribution with approximately equal numbers of observations above and below the middle is called a symmetrical distribution. A distribution that is not symmetrical (i.e., a distribution in which one side is more spread out than the other, like a tail) is called a skewed distribution. Specifically, a distribution with fewer scores to the left of the center is called skewed to the left or negatively skewed; a distribution with fewer scores to the right of the center is called skewed to the right or positively skewed.
- A floor effect occurs when what is being measured has a lower limit, causing many of the scores to "pile up" at the low end of the distribution. A ceiling effect occurs when what is being measured has an upper limit, causing many of the scores to "pile up" at the high end of the distribution.
- Kurtosis refers to the degree to which the tails of a distribution are "heavy" or "light." A distribution in which many of the scores are in the tails is known as a heavy-tailed distribution whereas a distribution in which few of the scores are in the tails is known as a light-tailed distribution.
- The normal curve is a unimodal, symmetrical curve with average tails.
