Analyzing Quantitative Data: Descriptive Statistics

• Nominal measurement — the classification of characteristics into mutually exclusive categories
• Ordinal measurement — the ranking of objects based on their relative standing to each other on an attribute
• Interval measurement — indicating not only the ranking of objects but the amount of distance between them
• Ratio measurement — distinguished from interval measurement by having a rational zero point
• Descriptive statistics enable researchers to summarize and describe quantitative data.
• In frequency distributions, which impose order on raw data, numeric values are ordered from lowest to highest, accompanied by a count of the number (or percentage) of times each value was obtained
• A skewed distribution is asymmetric, with one tail longer than the other.
• In a positively skewed distribution the long tail points to the right (e.g., personal income); in a negatively skewed distribution the long tail points to the left (e.g., age at death).
• Measures of central tendency are indexes, expressed as a single number, that represent the average or typical value of a set of scores.
• The mode is the value that occurs most frequently in the distribution
• Median is the point above which and below which 50% of the cases fall
• Mean is the arithmetic average of all scores.
• The mean is usually the preferred measure of central tendency because of its stability.
• Measures of variability — how spread out the data are—include the range, semiquartile range, and standard deviation.
• The range is the distance between the highest and lowest scores
• Standard deviation indicates how much, on average, scores deviate from the mean.
• The variance is equal to the standard deviation squared.