Define and know when to calculate three measures of central tendency.
The measure of central tendency that is calculated for a data set is determined by the level of measurement and the shape of the data set. A mean, M, can be calculated for interval- or ratio-level data that are not skewed or multimodal. The median, Mdn, is the score associated with the case that separates the top half of scores from the bottom half of scores. Medians can be calculated for ordinal-, interval-, or ratio-level data. The mode, the score that occurs most frequently, is the only measure of central tendency that can be calculated for nominal-level data. Modes can also be calculated for ordinal-, interval-, or ratio-level data. When there are multiple options for which measure of central tendency to choose, select the one that conveys the most information and takes the shape of the data set into consideration.
Define variability and know how to calculate four different measures of it.
Variability refers to how much spread there is in a set of scores. All four measures of variability are for interval- or ratio-level data. The range tells the distance from the smallest score to the largest score and is heavily influenced by outliers. The interquartile range, IQR, tells the distance covered by the middle 50% of scores. The IQR provides information about both central tendency and variability. Variance uses the mean squared deviation score as a measure of variability; standard deviation is the square root of variance and gives the average distance that scores fall from the mean. The larger the standard deviation, the less clustered scores are around the mean.
There is usually more variability in the population than in a sample. Population variance and standard deviation are abbreviated as σ2 and σ; sample variance and standard deviation as s 2 and s. The sample variance and standard deviation are “corrected” to approximate population values more accurately.