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Measures of Central Tendency Parentheses Exponents Multiplication or division Addition or subtraction *remember that signs form the skeleton of the formula ◦ X + Y / 2 (divide y by 2 and add to x) ◦ X + Y (add X and Y, then divide by 2) 2 Number that best represents a group of scores Represents the “typical” individual Describes a large amount of data with a single number No single measure is best Mean Median Mode Each gives different information about a group of scores A measure of where most values tend to fall in a dataset What we often refer to as an “average” Sum the values in a group & divide by number of values *Every score is represented X = ΣX/n X= mean value of a group of scores Σ = summation sign X = each score in the set n = sample size in set . Data: 41, 38, 56, 19, 31, 14, 52, 35, 34, 10, 38, 39, 20 1. 2. 3. 4. Most reliable and most often used Isn’t necessarily an actual score Strongly influenced by outliers Sum of the deviations equals zero Score (X) X-X 1 -2.56 5 1.44 2 -1.56 1 -2.56 2 -1.56 12 8.44 3 -.56 2 -1.56 4 0.44 SUM -.04 Multiply the value by the frequency of occurrence for each value, sum all the values, then divide by total frequency First Sample Second Sample n = 12 n=8 M=6 M=7 ΣX = 72 ΣX = 56 Combined Sample n = 20 ΣX = 128 M = 6.4 Midpoint in a set of scores 50% below and 50% above the median value No formula to compute List values in order, from lowest to highest & find the middle score If there are 2 middle scores, find the mean of these 2 scores Data: 41, 38, 56, 19, 31, 14, 52, 35, 34, 10, 38, 39, 20 The median is not sensitive to extreme scores and can be the most accurate centermost value (i.e., average) Means can skew due to extreme scores Value that occurs most frequently No formula to compute List all values once, tally the number of times each occurs, find the value that occurs most frequently Can have bimodal or multimodal sets Only way to capture an average for nominal data Data: 41, 38, 56, 19, 31, 14, 52, 35, 34, 10, 38, 39, 20 Nominal data can only be described with the mode The mean is usually the most precise with interval/ratio data Median is best in the presence of extreme values or if some values are imprecise *You might report more than one 1. When you have extreme scores or skew 2. When you have undetermined values 3. When you have an ordinal scale 1. When you have a nominal scale (and sometimes ordinal) 2. When you have discrete variables 3. When you are interested in describing the shape of a distribution When asked to write as you would for a journal ◦ Write the statistic of central tendency to 2 decimal places ◦ Clearly state what you are reporting ◦ Include the units of measurement The mean time to run a mile was 2.7 minutes The median home price in Texas is $80,000. When asked to interpret a finding “for someone unfamiliar with statistics” ◦ Describe the meaning of the statistic rather than using jargon ◦ Include the units of measurement The average runner completed a mile in about 2.7 minutes The middlemost home price in Texas is $80,000