Key Terms in Statistics: Chapters 1, 2, 3, and 4

Posted on Aug 23, 2024 in Mathematics

Chapter 4: Measures of Central Tendency and Skew

Measures of central tendency represent the center of a distribution. The most common measures are:

Mean: The average score, calculated by summing all scores and dividing by the total number of scores. Represented by ‘x̄’ for a sample and ‘μ’ for a population.
Median: The middle score when scores are arranged in numerical order. If there’s an even number of scores, the median is the average of the two middle scores.
Mode: The most frequently occurring score in a distribution.

Skew describes the shape of a distribution when graphed.

Statistics is a branch of applied mathematics using numbers to describe and analyze research data.

Hypothesis: A testable prediction about the relationship between variables.
Null Hypothesis: Predicts no relationship or change in behavior.
Research Hypothesis: Predicts a relationship or change in behavior.
Variables: Events or qualities that can assume more than one value.
Independent Variable: The factor manipulated by the experimenter.
Dependent Variable: The behavior measured and influenced by the independent variable.
Extraneous Variable: Any variable that can vary alongside the independent variable and needs to be controlled.
Population: All members of a specified group.
Sample: A smaller, representative group selected from the population.
Parameters: Statistics describing population values.
Estimates: Statistics from samples used to describe population values.

Nominal Scale: Categorizes data based on names or qualities.
Ordinal Scale: Ranks data in order but doesn’t measure the difference between ranks.
Interval Scale: Ranks data and measures the difference between ranks, but lacks a meaningful zero point.
Ratio Scale: Has all the properties of the previous scales and includes a meaningful zero point.

Raw Data: Unorganized, collected scores or numbers.
Ranked Distribution: Scores arranged in order from highest to lowest.
Simple Frequency Distribution: Lists all possible score values and their frequencies.
Frequency (f): The number of times a score occurs.
Grouped Frequency Distribution: Combines raw data into equal-sized groups called class intervals.

Class Intervals: Equal-sized groups of raw data.
Apparent Limits: The limits of a class interval in the original data units.
Range: The difference between the highest and lowest scores.
Real Limits: The true boundaries of a class interval, extending 0.5 units above and below the apparent limits.
Midpoint: The average or center of a class interval.
Cumulative Frequency (cum f): The total number of scores below the upper real limit of an interval.
Relative Frequency (rel f): The proportion of scores within a class interval.
Cumulative Percent (cum %): The percentage of scores below the upper real limit of an interval (percentile).
Cumulative Relative Frequency (cum rel f): The total proportion of scores below the upper real limit of an interval.

Axes: The horizontal and vertical lines of a graph.
X-axis (Abscissa): The horizontal line, typically representing the independent variable or score values.
Y-axis (Ordinate): The vertical line, typically representing the frequency or dependent variable.

Frequency Histogram: A bar graph showing the frequency of each class interval.
Frequency Polygon: A line graph connecting the midpoints of each class interval, showing frequency.
Relative Frequency Polygon: Similar to a frequency polygon, but using relative frequencies on the y-axis.
Cumulative Frequency Polygon: Shows the cumulative frequency at the upper real limit of each class interval.
Cumulative Relative Frequency Polygon: Shows the cumulative relative frequency at the upper real limit of each class interval.
Cumulative Percent Polygon (Percentile): Shows the cumulative percentage of scores below the upper real limit of each class interval.
Stem-and-Leaf Diagram: Visually displays data by separating each score into a stem (leading digits) and a leaf (final digit).