Central Tendency

Central Tendency

A summary measure describing the center, middle, or most typical score of a distribution; defined using three main metrics: mean, median, and mode. (Slide 3; Transcript 00:03:06, 00:07:08; Textbook p. 61)

Mean

The average score calculated by summing all values and dividing by the total number of observations, representing the distribution's center of gravity; it is appropriate for numeric data but highly sensitive to extreme tail values. (Slide 3, 4; Transcript 00:08:47, 00:15:23; Textbook pp. 61, 64)

Median

The middle score that divides an ordered distribution in half (50th percentile); highly robust against extreme outliers and especially useful for ordinal data, binned responses, or skewed numeric variables. (Slide 5, 6; Transcript 00:09:11, 00:16:07, 00:27:52; Textbook pp. 62-64)

Mode

The most frequently occurring score or peak value in a distribution; a distribution can have single or multiple modes, making it uniquely suited for nominal or categorical variables. (Slide 7, 8; Transcript 00:11:10, 00:12:17, 00:24:14, 00:35:54; Textbook pp. 67-68)

Symmetric Distribution Central Tendency

A distribution where the left and right halves mirror each other, resulting in the mean, median, and mode being equal and located at the exact center. (Slide 9; Transcript 00:14:24; Textbook p. 64)

Positively Skewed Distribution Central Tendency

An asymmetric distribution with a long tail extending toward higher positive values, which pulls the mean higher than the median and mode (Mode < Median < Mean), as seen in NBA salaries and morning sickness duration. (Slide 10; Transcript 00:17:01, 00:18:45, 00:22:08, 00:48:42; Textbook p. 64)

Negatively Skewed Distribution Central Tendency

An asymmetric distribution with a long tail extending toward lower negative values, which pulls the mean lower than the median and mode (Mean < Median < Mode), as seen in Index of Current Economic Conditions scores. (Slide 10; Transcript 00:14:47, 00:15:38, 00:43:53; Textbook p. 64)

Population Parameter

A fixed numerical characteristic describing an entire target population (denoted by Greek letters like mu for population mean); it exists theoretically but is practically unobservable due to incomplete population access. (Slide 12, 13; Transcript 00:52:44, 00:55:09; Textbook p. 151)

Sample Estimate

A numerical value calculated from a sample subset (e.g., sample mean x-bar) used to approximate the unknown population parameter. (Slide 12, 13; Transcript 00:53:45, 00:57:31; Textbook p. 151)

Sampling Error

The numerical difference between a sample estimate and the true population parameter, calculated as Sample Mean minus Population Mean (x-bar - mu); it reflects random variation across samples and can be positive, negative, or zero. (Slide 13; Transcript 01:00:10, 01:02:35, 01:03:41; Textbook p. 151)

Monte Carlo Simulation

A computer-based simulation technique that repeatedly draws random samples from a defined hypothetical population distribution to empirically demonstrate sampling error and sampling distributions. (Transcript 01:04:14, 01:05:49; Textbook p. 158)

How is the median calculated when a dataset contains an even number of scores?

Sort all scores in ascending order, locate the two middle values, and calculate their average. (Slide 5; Transcript 00:09:38; Textbook pp. 62-63)

Why is the mean used more widely in psychological research than the median or mode?

Because the mean is mathematically easier to analyze in standard inferential statistical procedures like t-tests and ANOVA, whereas median and mode require more complex non-parametric methods. (Slide 11; Transcript 00:08:04, 00:49:34; Textbook pp. 61, 64)

What does a bimodal distribution indicate about a dataset?

It indicates the presence of two distinct sub-populations mixed within the same sample, each having its own typical score peak. (Slide 8; Transcript 00:12:17, 00:12:41; Textbook p. 68)

Summation Notation

The uppercase Greek letter sigma used in statistical formulas as a mathematical shorthand to denote adding together a sequence of values across observations. (Textbook p. 62)

Law of Large Numbers

A fundamental statistical law stating that as the sample size increases, the sample mean becomes increasingly close to the true population mean. (Textbook p. 158)

Simple Random Sample

A sampling method in which every individual in the population has an equal probability of being selected into the sample. (Textbook p. 151)

Selection Bias

A systematic error in sampling where certain individuals or groups in a population are more or less likely to be included in a sample than others, creating an unrepresentative sample. (Textbook pp. 151-152)