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OhioMaths

Statistics and Probability

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

How do you measure the center and the spread of a data set, and when is the mean better than the median, and the IQR better than the range?

Compute and compare measures of center (mean, median) and spread (range, interquartile range, and informally standard deviation), and choose appropriate measures accounting for outliers (Ohio S-ID.2, S-ID.3).
An Ohio Algebra I answer on center and spread (S-ID.2, S-ID.3): computing mean and median, range and interquartile range, why outliers pull the mean, and choosing resistant measures when data is skewed.
12 min answer →

What does the correlation coefficient r tell you about a linear relationship, and why does correlation not prove causation?

Interpret the correlation coefficient of a linear fit and distinguish correlation from causation, recognizing lurking variables (Ohio S-ID.8, S-ID.9).
An Ohio Algebra I answer on correlation (S-ID.8, S-ID.9): what the correlation coefficient r measures, reading its sign and strength, and why a strong correlation does not prove one variable causes the other.
11 min answer →

How do you represent a set of one-variable data with dot plots, histograms, and box plots, and what does each display show about the distribution?

Represent data with dot plots, histograms, and box plots, and describe the shape of a distribution including skew, symmetry, and outliers (Ohio S-ID.1).
An Ohio Algebra I answer on representing one-variable data (S-ID.1): building and reading dot plots, histograms, and box plots, what the five-number summary means, and describing shape, skew, and outliers.
12 min answer →

How do you fit a line to a scatter plot, and how do you interpret the slope and intercept of a line of best fit in context?

Represent two-variable data on a scatter plot, fit a linear model (line of best fit), and interpret the slope and intercept in context, using the model to predict (Ohio S-ID.6, S-ID.7).
An Ohio Algebra I answer on scatter plots and lines of best fit (S-ID.6, S-ID.7): plotting paired data, fitting a trend line, interpreting slope as a rate and intercept as a starting value, and predicting from the model.
12 min answer →

How do you read a two-way frequency table, and what is the difference between joint, marginal, and conditional relative frequencies?

Summarize categorical data in two-way frequency tables and interpret joint, marginal, and conditional relative frequencies, recognizing possible associations (Ohio S-ID.5).
An Ohio Algebra I answer on two-way frequency tables (S-ID.5): reading counts and totals, computing joint, marginal, and conditional relative frequencies, and judging whether two categorical variables are associated.
12 min answer →