Glossary
Bimodal
A bimodal distribution has two distinct peaks, suggesting two different clusters or groups within the data.
Example:
The distribution of commute times for employees at a company might be bimodal if many live very close and many live very far, with fewer in between.
Gaps
Gaps are large spaces or intervals between data points in a distribution, which can suggest the presence of distinct subgroups or unusual data collection.
Example:
A histogram of house prices in a city might show a gap between affordable homes and luxury mansions, indicating two very different housing markets.
Interquartile Range (IQR)
The Interquartile Range (IQR) is the range of the middle 50% of the data, calculated as the difference between the third quartile (Q3) and the first quartile (Q1).
Example:
If the first quartile of student heights is 64 inches and the third quartile is 70 inches, the IQR is 6 inches, representing the spread of the middle half of students.
Left-skewed (Negatively Skewed)
A distribution is left-skewed if its tail extends further to the left, meaning there are a few unusually low values. Here, the mean is typically less than the median.
Example:
The scores on an easy quiz might be left-skewed, with most students scoring high marks and only a few scoring very low.
Mean
The mean is the arithmetic average of a dataset, calculated by summing all values and dividing by the number of values.
Example:
To find the mean number of hours students slept, you would add up all their reported sleep times and divide by the number of students.
Median
The median is the middle value in an ordered dataset, dividing the data into two equal halves.
Example:
If you list the ages of five friends as 16, 17, 18, 19, 20, the median age would be 18.
Mode
The mode is the value or values that appear most frequently in a dataset, represented by the peak(s) in a histogram.
Example:
In a survey of favorite ice cream flavors, 'chocolate' might be the mode if it was chosen by more people than any other flavor.
Multimodal
A multimodal distribution has more than two distinct peaks, indicating multiple clusters or groups within the data.
Example:
If you plot the ages of people attending a children's concert, you might see a multimodal distribution with peaks for young children, parents, and grandparents.
Outliers
Outliers are data values that are significantly higher or lower than the majority of the other data points in a distribution.
Example:
If a student scores a 100 on a test where everyone else scored between 60 and 80, that 100 would be considered an outlier.
Range
The range is a measure of spread calculated as the difference between the maximum and minimum values in a dataset.
Example:
If the highest temperature recorded in a week was 90°F and the lowest was 60°F, the range of temperatures for that week would be 30°F.
Right-skewed (Positively Skewed)
A distribution is right-skewed if its tail extends further to the right, meaning there are a few unusually high values. In this case, the mean is typically greater than the median.
Example:
The number of minutes students spend on a difficult AP Stats problem might be right-skewed, with most finishing quickly but a few struggling for a much longer time.
Skewed
A skewed distribution has a tail that stretches out more on one side than the other, indicating an imbalance in the data.
Example:
When looking at the distribution of household incomes, you'll likely see a skewed shape, as a few very high incomes pull the tail to the right.
Standard Deviation
Standard deviation measures the typical distance or average spread of data points from the mean of the distribution.
Example:
A small standard deviation for test scores means most students scored very close to the average, while a large one indicates scores were widely spread out.
Symmetry
A distribution is symmetric if its left and right sides are approximate mirror images of each other when folded in half.
Example:
The distribution of heights for adult males often shows a symmetric shape, with most men clustered around the average height and fewer at very short or very tall extremes.
Uniform
A uniform distribution has no clear peaks, meaning all values or ranges of values occur with roughly the same frequency.
Example:
Rolling a fair six-sided die many times would result in a uniform distribution of outcomes, as each number (1-6) is equally likely to appear.
Unimodal
A unimodal distribution has a single, distinct peak, indicating one most frequent value or range of values.
Example:
A histogram showing the distribution of test scores for a typical class often appears unimodal, with most scores clustering around a single average.