Data Representations
This data display uses dots placed above a number line to show frequencies and is best suited for small data sets
What is a dot plot?
A distribution where the left and right sides are mirror images of each other across a central vertical line
What is a symmetric distribution?
Calculated as Q3 - Q1, this statistic measures the spread of the middle 50% of the data.
What is the Interquartile Range (IQR)?
A data point that is substantially higher or lower than the rest of the observations in a data set
What is an outlier?
When comparing two distributions that are symmetric with no outliers, these two summary statistics should be used to evaluate center and spread
What are the mean and standard deviation?
This visual display uses adjacent bars corresponding to intervals/ranges and is ideal for viewing overall patterns or trends in large numerical data sets
What is a histogram?
In this distribution shape, the tail extends off toward higher values on the right, pulling the mean to be greater than the median
What is a skewed right distribution?
This measure of center is preferred when summarizing data that is symmetric and free of extreme values or outliers
What is the mean?
According to the standard 1.5 * IQR rule, any data point less than this mathematical expression is considered an unusually low outlier
What is Q1 - (1.5 * IQR)?
When comparing two distributions that are skewed or contain outliers, these two summary statistics should be used to evaluate center and spread
What are the median and Interquartile Range (IQR)?
These five specific values make up the five-number summary that forms a box plot.
What are the Minimum, First Quartile (Q1), Median (Q2), Third Quartile (Q3), and Maximum?
In a distribution that is skewed left (tail stretching toward lower values), this measure of center is strictly less than the median
What is the mean?
This measure of center is preferred when summarizing skewed data because extreme values do not easily distort it
What is the median?
For a dataset with Q1 = 22 and Q3 = 29, this exact numerical value represents the upper boundary (Q3 + (1.5 *IQR)) for outliers
What is 39.5?
If a constant value of 5 is added to every observation in a dataset, this is the exact effect on the measures of center (mean and median)
What is they increase by 5?
For the ordered data set {20, 24, 28, 35, 55, 58, 59, 66, 67, 67, 92}, this value is the median (Q2)
What is 58?
A distribution that features two distinct, prominent peaks
What is a bimodal distribution?
This measure of variability tells you how far data points typically deviate from the mean, and is best paired with symmetric distributions
What is standard deviation?
When a high extreme value or outlier is introduced, these two summary statistics increase significantly, whereas median and IQR remain mostly stable
What are the mean and standard deviation?
If a constant value of 5 is added to every data point, this key characteristic of the overall distribution remains completely unchanged
What is the shape of the distribution (and measures of variability like IQR/standard deviation)?
This graphical representation is specifically suited for highlighting the overall spread, comparing multiple distributions side-by-side, and identifying potential outliers
What is a box plot?
A distribution where data values or intervals occur with roughly equal frequency across the range, producing a rectangular profile
What is a uniform distribution?
When comparing two drivers or groups with identical average/mean scores, a larger value for this statistic indicates greater variation or less consistency
What is standard deviation?
When an incorrectly recorded outlier (such as a length mis-entered as 122 cm) is removed from a data set, this is what happens to the standard deviation
What is it decreases (becomes smaller)?
In an experiment comparing two situations where both distributions are symmetric with equal means, but Situation B's data points are spread further across the number line, Situation B has a greater value for this statistic
What is standard deviation (or variability)?