What are the three main data displays and when do you use each?

A dot plot stacks a dot for each value and suits small data sets. A histogram groups data into intervals and shows frequency as touching bars, good for larger sets. A box plot displays the five-number summary (minimum, Q1, median, Q3, maximum), ideal for comparing groups. Each answers a different question about one-variable numerical data.

How do you describe the shape of a distribution?

Name it for the direction of the long tail. A long tail to the right is skewed right (most data on the left); a long tail to the left is skewed left (most data on the right); balanced halves are symmetric. The skew is named for the tail, not the crowded end, and the mean is pulled toward the tail while the median resists.

When should you use the median instead of the mean?

Use the median for skewed data or data with outliers, because the median depends only on the middle position and resists extreme values, while the mean is pulled toward outliers. For roughly symmetric data with no outliers, the mean and standard deviation are appropriate. Pair the median with the interquartile range for spread.

What is the difference between joint, marginal, and conditional relative frequency?

All three are a part over a whole; the whole differs. A joint relative frequency is a single cell over the grand total. A marginal relative frequency is a row or column total over the grand total. A conditional relative frequency is a cell over its row or column total, which restricts attention to one group. The wording, of everyone versus of the seniors, tells you the denominator.

How do you interpret the slope and intercept of a line of best fit?

The slope is the predicted change in y for each one-unit increase in x, and the y-intercept is the predicted y when x equals 0. Because the line models a trend, interpretations use words like predicted or associated. Predicting within the data range (interpolation) is reliable; predicting far beyond it (extrapolation) is risky.

Why does correlation not imply causation?

A correlation shows two variables move together, but that pattern is consistent with several explanations: X causes Y, Y causes X, a lurking third variable causes both, or coincidence. Ice-cream sales and drownings correlate because summer heat drives both, not because one causes the other. Only a controlled experiment can establish causation.

FloridaMaths

B.E.S.T. Algebra 1 EOC: a complete guide to data analysis and probability

A deep-dive B.E.S.T. Algebra 1 EOC guide to data analysis (MA.912.DP): dot plots, histograms, and box plots and distribution shape, center and spread with outliers, two-way frequency tables, scatter plots and lines of fit, and correlation versus causation. Part of the Statistics and Number System category, very gettable points.

Generated by Claude Opus 4.816 min readMA.912.DP.1, MA.912.DP.2, MA.912.DP.3Updated 2026-06-02

Reviewed by: AI editorial process; not yet individually human-reviewed

Jump to a section

What this category demands
Data displays and shape
Center and spread
Two-way frequency tables
Scatter plots and lines of fit
Correlation and causation
How this category is examined
Check your knowledge

What this category demands

This guide covers data analysis and probability (MA.912.DP), the statistics half of the Statistics and the Number System reporting category (about 19 percent of the test with the Number System). Students often neglect it, but the points are very gettable and lift a borderline score over Level 3. The skills are data displays and shape, center and spread, two-way tables, scatter plots and lines of fit, and correlation versus causation. Each dot-point page has its own practice: data displays and shape, comparing center and spread, two-way frequency tables, scatter plots and lines of fit, and correlation, residuals, and causation.

Data displays and shape

A dot plot shows each value; a histogram groups data into touching bins; a box plot shows the five-number summary (minimum, Q1, median, Q3, maximum). Shape is named for the long tail: a right tail is skewed right, a left tail is skewed left, balanced is symmetric.

Center and spread

The mean uses every value; the median uses only the middle position and resists outliers. Spread is the range (max minus min), the IQR ( $Q_3 - Q_1$ , resistant), or the standard deviation (typical distance from the mean). For skewed data or outliers, use the median and IQR; for symmetric data, the mean and standard deviation.

Two-way frequency tables

A two-way table cross-classifies categorical data. Joint relative frequency is a cell over the grand total; marginal is a margin total over the grand total; conditional is a cell over its row or column total. The wording sets the denominator.

Scatter plots and lines of fit

Describe a scatter plot by direction (positive or negative), strength (tight or loose), and form (linear or not). A line of best fit $\hat{y} = mx + b$ has a slope (predicted change in $y$ per unit $x$ ) and intercept (predicted $y$ at $x = 0$ ). Interpolation (within the data) is reliable; extrapolation (far beyond) is risky.

Correlation and causation

The correlation coefficient $r$ runs from $-1$ to $1$ : the sign is direction, the magnitude is strength of the linear association. Correlation does not imply causation, a lurking variable can drive both, and only a controlled experiment establishes cause. A residual is actual minus predicted $y$ ; a patternless residual plot means a line fits well.

How this category is examined

Number entry and equation editor. Compute a five-number summary, mean, median, IQR, relative frequency, residual, or a prediction from a line of fit.
Multiple choice and multiselect. Identify distribution shape, choose the resistant measure, interpret $r$ , or spot a correlation-causation error.
Table and GRID items. Complete two-way tables; read box plots, histograms, and scatter plots.

Check your knowledge

Work these as you would for credit on the computer-based test.

Find the five-number summary of $6, 8, 9, 10, 13, 15, 21$ . (2 points)
A distribution has a long left tail. What is its shape? (1 point)
Find the mean and median of $5, 6, 8, 9, 22$ . (2 points)
A data set has one extreme outlier. Which center is more representative? (1 point)
Of 60 students, 24 take art. What is the marginal relative frequency of art students? (1 point)
Of 30 seniors, 9 play music. What is the conditional relative frequency among seniors? (1 point)
A line of best fit is $\hat{y} = 4x + 20$ . What does the slope mean? (1 point)
Interpret a correlation coefficient of $r = -0.88$ . (1 point)
Ice-cream sales and sunburns are correlated. Name the likely lurking variable. (1 point)

Solutions

Step 1: Build the five-number summary for the data set

To find the five-number summary, first put the values in order and identify the median, then split the remaining values to find the quartiles. The median is the middle value, Q1 is the median of the lower half, and Q3 is the median of the upper half.

Order: $6, 8, 9, 10, 13, 15, 21$ . The 4th value is the median; the lower half is $6, 8, 9$ and the upper half is $13, 15, 21$ .

\text{Min} = 6,\quad Q_1 = 8,\quad \text{Median} = 10,\quad Q_3 = 15,\quad \text{Max} = 21

Final answer: Five-number summary: $6, 8, 10, 15, 21$ .

Step 2: Name the shape of a distribution with a long left tail

The shape is named for the direction of the long tail, not for where most of the data clusters. A long tail stretching to the left means the distribution is skewed left (also called negatively skewed).

Final answer: Skewed left.

Step 3: Compute the mean and median, and explain why they differ

The mean uses all five values and is pulled toward any extreme; the median uses only the middle position and resists extremes. When an outlier is present, the two measures will diverge, with the mean moving toward the outlier.

\text{Mean} = \frac{5 + 6 + 8 + 9 + 22}{5} = \frac{50}{5} = 10

The 3rd value in the ordered list is the median. The outlier 22 pulls the mean above the median.

\text{Median} = 8

Final answer: Mean $= 10$ ; median $= 8$ .

Step 4: Choose the better measure of center when an outlier is present

The median depends only on the middle position, so a single extreme value cannot drag it away from the bulk of the data. The mean uses every value and is therefore distorted by even one very high or very low score.

Final answer: The median, because it resists the outlier.

Step 5: Calculate the marginal relative frequency of art students

A marginal relative frequency compares a row or column total to the grand total. Here, 24 art students out of 60 total students gives the fraction of all students who take art.

\frac{24}{60} = 0.40

Final answer: $0.40$ (40%).

Step 6: Calculate the conditional relative frequency among seniors

A conditional relative frequency restricts the denominator to one group. Because the question asks "of the seniors," the denominator is the number of seniors, not the grand total.

\frac{9}{30} = 0.30

Final answer: $0.30$ (30%).

Step 7: Interpret the slope of the line of best fit

The slope of a line of best fit tells you how much the predicted $y$ value changes for each one-unit increase in $x$ . Because this is a model, interpretation uses words like "predicts" or "is associated with."

For $\hat{y} = 4x + 20$ , the slope is $4$ .

Final answer: Each one-unit increase in $x$ predicts an increase of about 4 in $y$ .

Step 8: Interpret a correlation coefficient of $r = -0.88$

The sign of $r$ gives direction and the magnitude gives strength. A value close to $-1$ means the points cluster tightly around a line that slopes downward, indicating a strong negative linear association.

Final answer: A strong negative linear association.

Step 9: Identify the lurking variable behind a spurious correlation

When two variables rise and fall together but neither causes the other, a lurking third variable often drives both. Hot, sunny weather increases outdoor activity and sun exposure, which independently raises both ice-cream purchases and sunburn rates.

Final answer: Hot, sunny weather (more sun exposure raises both).

Sources & how we know this

B.E.S.T. Mathematics Standards — Florida Department of Education (2020)
B.E.S.T. Algebra 1 EOC Computer-Based Practice Test — Florida Department of Education (2024)