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These statistical

These statistical techniques are calculated to determine the center of a distribution of data, and the central tendency that is calculated is determined by the level of measurement of the data (nominal, ordinal, interval, or ratio; see Exercise 1 ). The mode is a category or score that occurs with the greatest frequency in a distribution of scores in a data set. The mode is the only acceptable measure of central tendency for analyzing nominal-level data, which are not continuous and cannot be ranked, compared, or sub-jected to mathematical operations. If a distribution has two scores that occur more fre-quently than others (two modes), the distribution is called bimodal . A distribution with more than two modes is multimodal ( Grove, Burns, & Gray, 2013 ). The median ( MD ) is a score that lies in the middle of a rank-ordered list of values of a distribution. If a distribution consists of an odd number of scores, the MD is the middle score that divides the rest of the distribution into two equal parts, with half of the values falling above the middle score and half of the values falling below this score. In a distribu-tion with an even number of scores, the MD is half of the sum of the two middle numbers of that distribution. If several scores in a distribution are of the same value, then the MD will be the value of the middle score. The MD is the most precise measure of central ten-dency for ordinal-level data and for nonnormally distributed or skewed interval- or ratio-level data. The following formula can be used to calculate a median in a distribution of scores. Median()()MDN=+÷12 N is the number of scores ExampleMedianscoreth_N==+=÷=31311232216 ExampleMedianscoreth:.N==+=÷=404012412205 Thus in the second example, the median is halfway between the 20 th and the 21 st scores. The mean ( X ) is the arithmetic average of all scores of a sample, that is, the sum of its individual scores divided by the total number of scores. The mean is the most accurate measure of central tendency for normally distributed data measured at the interval and ratio levels and is only appropriate for these levels of data (Grove, Gray, & Burns, 2015). In a normal distribution, the mean, median, and mode are essentially equal (see Exercise 26 for determining the normality of a distribution). The mean is sensitive to extreme

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