Statistics Lecture 3 and 4 Review

This set of vocabulary flashcards covers essential statistics concepts from July 14th and 16th lectures (Lectures 3 and 4), including measures of central tendency, skewness, variability, Box Plots, Z-score conversions, and Standard Error.

Mean

The average of a set of observations, calculated using the formula $M = \frac{\sum X_i}{N}$. For example, with observations $8, 2, 5, 1, 9$, the result is $M = 5$.

Central Tendency

A measure used to determine the center of a distribution, typically represented by the Mean, Median, or Mode.

Left/Negative Skew

A distribution where the relationship between central tendency measures is $\text{Mean} < \text{Median} < \text{Mode}$.

No Skew

A distribution where the Mean, Median, and Mode are all the same value.

Right/Positive Skew

A distribution where the relationship between central tendency measures is $\text{Mode} < \text{Median} < \text{Mean}$.

Variability

A numerical way of describing how widely spread out the observations are in a distribution, commonly measured by variance, standard deviation, and range.

Range

A measure of variability calculated as $\text{Range} = X_{\text{highest}} - X_{\text{lowest}}$. Its limitation is that it cannot tell how much observations are clustered or spread out.

Inter-Quartile Range (IQR)

The distance between the $1^{\text{st}}$ ($25^{\text{th}}$ percentile) and $3^{\text{rd}}$ ($75^{\text{th}}$ percentile) quartiles, covering the middle $50\%$ of observations.

Calculating the IQR

A four-step process: 1. find median; 2. find the median of the higher observations ($3^{\text{rd}}$ quartile); 3. find the median of the lower observations ($1^{\text{st}}$ quartile); 4. subtract the $1^{\text{st}}$ quartile from the $3^{\text{rd}}$ quartile.

Box Plots

A visualization of the median, $3^{\text{rd}}$ quartile, $1^{\text{st}}$ quartile, and range (including outliers). The horizontal line represents the median, the top of the box is the $3^{\text{rd}}$ quartile, the bottom is the $1^{\text{st}}$ quartile, and the whiskers represent the range.

Positive Skew in Box Plots

A box plot characteristic where the Median is low.

Negative Skew in Box Plots

A box plot characteristic where the Median is high.

Low Variability

Indicates that observations tend to be closer to the Mean.

High Variability

Indicates that observations tend to be far from the Mean.

Deviation Score

The difference between an individual observation and the mean, expressed as $(X_i - M)$.

Z-score Formula

A formula used to convert a raw score to a standard score: $z = \frac{X - M}{SD}$.

Converting Z-score to a New Score

The process of finding a raw score from a z-score using the calculation $X = (z \times SD) + M$. For example, if $z = 2.5$, $M = 6.3$, and $SD = 2.1$, then $X = 11.55$.

Standard Error of the Mean

A statistical measure calculated using the formula $s_{\bar{X}} = \frac{s}{\sqrt{N}}$.