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. Most reliable and most often used  2. Isn’t necessarily an actual score  3. Strongly influenced by outliers  4. Sum of the deviations equals zero Score (X)X-X 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 Combined Sample n = 12n = 8n = 20 M = 6M = 7 ΣX = 72ΣX = 56ΣX = 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