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can be ranked are said to be on an ordinal scale, and can be put in order. For example, the highest scorer can be designated as “1,” the second highest as “2,” the third highest as “3,” etc. These numbers cannot be averaged. Number 1 could have scored 50 points higher than 2. Number 2 may have scored 4 points higher than 3. If there is a meaningful difference between each of the numbers, the numbers are said to be on an interval scale. For example, the difference between 32° Fahrenheit (F) and 42°F is 10°F. The difference between 64°F and 74°F is also 10°F. However, 64°F is not twice as hot as 32°F. When a meaningful ratio can be made with two numbers, the numbers are said to be on a ratio scale. The key difference between an interval scale and a ratio scale is that the ratio scale has a real or absolute zero point. For quantities of weight, volume, and distance, zero is a meaningful concept, whereas the meaning of 0°F is arbitrary.

Statistics is a field that involves the analysis of numerical data about representative samples of populations.

Descriptive Statistics

Numbers that summarize a set of research data obtained from a sample are called descriptive statistics. In general, descriptive statistics describe sets of interval or ratio data. After collecting data, psychologists organize the data to create a frequency distribution, an orderly arrangement of scores indicating the frequency of each score or group of scores. The data can be pictured as a histogram—a bar graph from the frequency distribution—or as a frequency polygon—a line graph that replaces the bars with single points and connects the points with a line. With a very large number of data points, the frequency polygon approaches a smooth curve. Frequency polygraphs are shown in Figure 6.1.

Measures of Central Tendency

Measures of central tendency describe the average or most typical scores for a set of research data or distribution. Measures of central tendency include the mode, median, and mean. The mode is the most frequently occurring score in a set of research data. If two scores appear most frequently, the distribution is bimodal; if three or more scores appear most frequently, the distribution is multimodal. The median is the middle score when the set of data is ordered by size. For an odd number of scores, the median is the middle one. For an even number of scores, the median lies halfway between the two middle scores. The mean is the arithmetic average of the set of scores. The mean is determined by adding up all of the scores, then dividing by the number of scores. For the set of quiz scores 5, 6, 7, 7, 7, 8, 8, 9, 9, 10; the mode is 7; the median is 7.5; the mean is 7.6. The mode is the least used measure of central tendency, but can be useful to provide a “quick and dirty” measure of central tendency especially when the set of data has not been ordered. The mean is generally the preferred measure of central tendency because it takes into account the information in all of the data points; however, it is very sensitive to extremes. The mean is pulled in the direction of extreme data points. The advantage of the median is that it is less sensitive to extremes, but it doesn’t take into account all of the information in the data points. The mean, mode, and median turn out to be the same score in symmetrical distributions. The two sides of the frequency polygon are mirror images as shown in Figure 6.1a. The normal distribution or normal curve is a symmetric, bell-shaped curve that represents data about how many human characteristics are dispersed in the population. Distributions where most of the scores are squeezed into one end are skewed. A few of the scores stretch out away from the group like a tail. The skew is named for the direction of the tail. Figure 6.1b pictures a negatively skewed distribution, and Figure 6.1c shows a positively skewed distribution. The mean is pulled in the direction of the tails, so the mean is lower than the median in a negatively skewed distribution, and higher than the median in a positively skewed distribution. In