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

## Chapter 4: Measures of Central Tendency and Skew

### Measures of Central Tendency

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.

#### Types of Distributions Based on Mode:

**Unimodal:**One mode.**Bimodal:**Two modes.**Multimodal:**More than two modes.

### Skew

Skew describes the shape of a distribution when graphed.

**Zero Skew:**Symmetrical distribution.**Positive Skew:**Tail points towards the positive direction (right).**Negative Skew:**Tail points towards the negative direction (left).

## Chapter 1: Introduction to Statistics

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

### Key Concepts in Research:

**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.

### Scales of Measurement:

**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.

## Chapter 2: Organizing and Summarizing Data

### Data Organization:

**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 (**The number of times a score occurs.*f*):**Grouped Frequency Distribution:**Combines raw data into equal-sized groups called class intervals.

### Key Terms in Frequency Distributions:

**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**The total number of scores below the upper real limit of an interval.*f*):**Relative Frequency (**The proportion of scores within a class interval.*rel f*):**Cumulative Percent (**The percentage of scores below the upper real limit of an interval (percentile).*cum %*):**Cumulative Relative Frequency (cum**The total proportion of scores below the upper real limit of an interval.*rel f*):

## Chapter 3: Graphing Data

### Components of a Graph:

**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.

### Types of Graphs:

**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).