Statistics Lecture 2: Central Tendency

Lecture 2: Central Tendency Descriptive Statistics: the presentation, organization, and summarization of data -​ Graphical representation, tables, demographic data Central Tendency: a value around which a data set is centered or clustered Measures of Central Tendency​ ​ ​ ​ ​ SKEW: 1.​ Mean (average) 2.​ Median 3.​ Mode Mean - the average score -​ Used for variables measured at the interval or ratio level -​ Calculate by adding all the numbers in a distribution and dividing by the number of observations Median - the middle value in an ordered array of numbers -​ Used for variables at the ordinal, interval, or ratio level Mode - the most frequent category -​ Used for variables measured at the nominal level, but can be used for ordinal, interval, and ratio levels -​ You can have more than one mode Histograms -​ Visual representations of the data frequencies -​ Includes normal distribution/bell shaped curve -​ Normal distributions the mean, median, and mode are equal Measures of Variability/Dispersion -​ Describes the spread of a set of data 1.​ Range 2.​ Variance 3.​ Standard Deviation Range -​ How far apart the scores are from the mean -​ Range = highest value - lowest value Variance -​ How spread out the data is (the average distance from the arithmetic mean) -​ Small variance = most scores close to the average -​ Large variance = scores are widely spread -​ Values will be squared Standard Deviation -​ -​ Square root of the variance Gives you information on the amount of variance Inter-Quartile Range -​ Not sensitive to extreme scores -​ Allows you to divide the distribution into quarters -​ The median is the 50th percentile -​ Values extend from 25-75% -​ Whisker plot ↓ Inferential Statistics: allows us to make predictions/inferences about a larger population based on the sample -​ Includes: Probability, Normal distribution, Population sample, Standard scores (z-scores) Parametric and Non-Parametric Statistics: parametric statistics are based on assumptions about the distribution from which the sample was taken. Non-parametric statistics are not based on assumptions. You use non-parametric to collect data from a sample that does not follow a specific distribution -​ Parametric statistic assumptions: -​ Random sample -​ Unbiased selection -​ Normal distribution of variable in population -​ Observations are independent of each other -​ Homogeneity of variance