Glossary
Interquartile Range (IQR)
A measure of statistical dispersion, calculated as the difference between the third quartile (Q3) and the first quartile (Q1). It represents the spread of the middle 50% of the data.
Example:
If the first quartile of student heights is 60 inches and the third quartile is 68 inches, the Interquartile Range is 8 inches, showing the spread of the middle half of heights.
Left-Skewed (Negatively Skewed)
A data distribution where the tail of the distribution extends to the left, indicating that most data values are concentrated on the higher end. In this shape, the mean is typically less than the median.
Example:
A distribution of exam scores where most students scored very high, but a few scored very low, would likely be left-skewed.
Mean
The average of a dataset, calculated by summing all values and dividing by the number of values. It represents the balancing point of the data.
Example:
If a student scores 85, 90, and 95 on three tests, their mean score is 90.
Median
The middle value in a dataset when the data is ordered from least to greatest. If there's an even number of values, it's the average of the two middle values.
Example:
In the dataset {10, 12, 15, 16, 18}, the median is 15.
Mode
The value that appears most frequently in a dataset. A dataset can have one, multiple, or no modes.
Example:
In a survey of favorite colors, if "blue" was chosen by 15 people, "red" by 10, and "green" by 5, then "blue" is the mode.
Outliers
Extreme values in a dataset that are significantly different from other data points. They can disproportionately influence certain statistical measures.
Example:
In a list of house prices for a neighborhood, a single mansion priced at 300,000 would be an outlier.
Range
A measure of spread calculated as the difference between the maximum and minimum values in a dataset. It indicates the total span of the data.
Example:
For test scores ranging from 60 to 98, the range is 38 points.
Right-Skewed (Positively Skewed)
A data distribution where the tail of the distribution extends to the right, indicating that most data values are concentrated on the lower end. In this shape, the mean is typically greater than the median.
Example:
Income distribution in most countries is often right-skewed, with many people earning lower incomes and a few earning very high incomes.
Standard Deviation
A measure of the average amount of variability or dispersion of data points around the mean. A higher standard deviation indicates greater spread.
Example:
If two classes have the same average test score, but one has a much higher standard deviation, it means scores in that class were more spread out from the average.
Symmetric Distributions
Data distributions where the data is evenly distributed around a central point, meaning the left and right sides are mirror images. In such distributions, the mean, median, and mode are approximately equal.
Example:
A perfectly balanced bell curve representing student heights in a large population would be a symmetric distribution.