Grade 10 Math MCAS: a complete guide to the Statistics and Probability category

What this category demands

The Statistics and Probability category on the Grade 10 MCAS, drawn from the S-ID, S-IC, and S-CP standards, is largely about interpretation. It asks you to summarize data with center and spread, read scatterplots and two-way tables, fit and use a line of best fit, compute probabilities, and reason critically about claims, samples, and outliers. Many items are short-answer or reasoning, so clear explanations matter. This guide ties together the dot-point pages, each with its own practice: one-variable data and distributions, two-variable data and scatterplots, linear regression and correlation, probability rules and models, and interpreting data and avoiding traps.

One-variable data

The mean is the average; the median is the middle of the ordered data (average the two middle values for an even count). Spread is the range (max minus min) or the IQR ($Q_3 - Q_1$, the middle 50%). A box plot shows the five-number summary. When data has outliers or skew, the median and IQR are more representative, because the mean and range are pulled by extremes. In right-skewed data, mean $>$ median.

Two-variable data

A scatterplot shows how two variables relate; describe it by form (linear or curved), direction (positive rising, negative falling), and strength (tight or scattered). Watch for clusters and outliers. A two-way frequency table cross-tabulates two categorical variables; read totals by adding the relevant cells, and form relative frequencies by dividing by a row, column, or grand total.

Linear regression and correlation

A line of best fit $y = mx + b$ models the trend: the slope is the predicted change in $y$ per unit of $x$, and the intercept is the predicted $y$ at $x = 0$. Predict by substituting an $x$-value, but treat the result as an estimate and beware extrapolation. The correlation coefficient $r$ runs from $-1$ to $1$, measuring strength and direction. Crucially, correlation is not causation.

Probability

Probability is favorable over total outcomes, from 0 to 1. The complement rule is $P(\text{not } A) = 1 - P(A)$, often the fast route to "at least one". The addition rule for "or" is $P(A) + P(B) - P(A \text{ and } B)$, simplifying to a sum for mutually exclusive events. The multiplication rule for "and" with independent events is $P(A) \times P(B)$. Add for "or", multiply for "and".

Interpreting data critically

Choose the appropriate measure (median for skew or outliers), and reason about how an outlier inflates the mean and range but barely moves the median and IQR. Spot misleading graphs (a truncated axis exaggerates differences) and biased samples (a non-random or convenience sample cannot be generalized). A random sample is what supports a valid conclusion.

How this category is examined

• Selected-response (1 point, calculator usually allowed). A median, an IQR, a probability, a scatterplot description, a two-way table total.
• Short-answer (1 point). A single computed statistic or probability, scored by exact match.
• Constructed-response and reasoning (multi-point). Justify the choice of a measure, interpret slope and intercept, explain an outlier's effect, or identify and explain a sampling bias.

Check your knowledge

Work these as you would for credit.

1. Find the median of $5, 9, 11, 14, 14, 20$. (1 point)
2. A data set has $Q_1 = 30$, $Q_3 = 52$. Find the IQR. (1 point)
3. Describe the association if a scatterplot's points fall tightly from upper left to lower right. (1 point)
4. For the line of best fit $y = 1.5x + 4$, interpret the slope in context if $x$ is weeks and $y$ is plant height in cm. (2 points)
5. A correlation of $r = -0.88$ describes what kind of relationship? (1 point)
6. A die is rolled. Find $P(\text{a 2 or a 5})$. (2 points)
7. Two coins are flipped. Find $P(\text{at least one head})$ using the complement. (2 points)
8. A survey is taken only of gym members about exercise habits in the town. Why is it biased? (2 points)