Which data display should you use?

Use a dot plot for small data sets where exact values matter. Use a histogram for larger sets where the overall shape is what counts; it groups values into equal intervals and shows frequency. Use a box plot to display the five-number summary and to compare spread and center across groups. Each display trades detail for summary differently.

What is the difference between the mean and the median, and which resists outliers?

The mean is the sum divided by the count, using every value's size, so an outlier pulls it. The median is the middle value of the ordered data, depending only on position, so it resists outliers. For skewed data or data with outliers, the median is the more representative measure of center, and the interquartile range is the resistant measure of spread.

What are joint, marginal, and conditional relative frequencies?

In a two-way frequency table, a joint relative frequency is one cell divided by the grand total, a marginal relative frequency is a row or column total divided by the grand total, and a conditional relative frequency is a cell divided by its row or column total. The denominator is what distinguishes them: grand total for joint and marginal, group total for conditional.

What does the slope of a line of best fit mean?

The slope is the predicted change in the response variable per one-unit change in the explanatory variable, stated with units, for example about 6 more points per additional hour studied. The y-intercept is the predicted response when x is zero. Because a model describes a trend, phrase interpretations as associated with or predicted, not as a guarantee.

What does the correlation coefficient tell you?

The correlation coefficient r, between negative 1 and 1, measures the strength and direction of a linear relationship. The sign gives the direction (positive rises together, negative falls), and the size gives the strength (near plus or minus 1 is strong, near 0 is weak). It measures linear fit only, so a strong curved pattern can still have an r near zero.

Why does correlation not imply causation?

Two variables can move together without one causing the other, because of a lurking variable (a hidden common cause), coincidence, or reverse causation. Ice cream sales and drownings correlate because both rise with hot weather. To establish causation you need a controlled experiment that isolates the variable, not just a strong correlation.

LouisianaMaths

Louisiana LEAP 2025 Algebra I: a complete guide to statistics and probability (S-ID)

A deep-dive Louisiana LEAP 2025 Algebra I guide to statistics: representing data with dot plots, histograms, and box plots (S-ID.A.1), measures of center and spread with outliers (S-ID.A.2/A.3), two-way frequency tables (S-ID.B.5), fitting linear models to scatter plots (S-ID.B.6), and interpreting correlation versus causation (S-ID.C).

Generated by Claude Opus 4.814 min readA1: S-ID.A, S-ID.B, S-ID.CUpdated 2026-06-02

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

Jump to a section

What this module covers
Representing data
Center and spread
Two-way frequency tables
Scatter plots and linear models
Correlation and causation
How this module is examined
Check your knowledge

What this module covers

This guide covers statistics and probability on the Louisiana LEAP 2025 Algebra I test, the Additional and Supporting Content category built from S-ID: representing data with dot plots, histograms, and box plots (S-ID.A.1), measures of center and spread with outliers (S-ID.A.2, S-ID.A.3), two-way frequency tables (S-ID.B.5), fitting linear models to scatter plots (S-ID.B.6), and interpreting the correlation coefficient versus causation (S-ID.C). The calculator can compute statistics on the calculator sessions, but you interpret them. Each dot-point page has its own practice: representing data distributions, comparing center and spread, two-way frequency tables, scatter plots and linear models, and correlation and the correlation coefficient.

Representing data

A dot plot shows each value (small sets); a histogram groups values into bins and shows frequency (larger sets, shape); a box plot displays the five-number summary (minimum, Q1, median, Q3, maximum).

Center and spread

Center: mean (sum over count) and median (middle value). Spread: range (max minus min) and IQR (Q3 minus Q1).

Two-way frequency tables

A two-way table cross-classifies two categorical variables with row, column, and grand totals. A joint frequency divides a cell by the grand total; a marginal divides a total by the grand total; a conditional divides a cell by its row or column total.

Scatter plots and linear models

Describe a scatter plot's association (direction, strength, form), fit a line of best fit $y = mx + b$ , and interpret the slope (predicted change per unit) and intercept (predicted value at $x = 0$ ). Interpolation (inside the range) is reliable; extrapolation (outside) is risky.

Correlation and causation

The correlation coefficient $r$ (from $-1$ to $1$ ) measures the strength and direction of a linear relationship: sign for direction, size for strength. Correlation does not imply causation, a lurking variable, coincidence, or reverse causation may explain it.

How this module is examined

Equation response. Compute a five-number summary, mean, median, IQR, or a relative frequency.
Type II reasoning. Interpret a slope, correlation, or why correlation is not causation.
Multiple choice. Match displays to purposes, interpret $r$ , or pick the resistant measure.
Calculator sessions. Use the embedded calculator for statistics and regression, then interpret.

Check your knowledge

Work these as you would for credit on the online test.

Find the five-number summary of $4, 6, 7, 7, 9, 12, 15$ . (2 points)
Which display best shows values grouped into equal intervals? (1 point)
Find the mean and median of $3, 5, 7, 9, 26$ . (2 points)
Which measure of center is least affected by an outlier? (1 point)
Of 100 students, 30 juniors prefer pizza. What is that joint relative frequency? (2 points)
Of 40 juniors, 30 prefer pizza. What is that conditional relative frequency? (2 points)
A best-fit line is $y = 6x + 50$ (hours vs score). Interpret the slope. (2 points)
Using $y = 6x + 50$ , predict the score at 5 hours. (2 points)
A linear fit has $r = -0.95$ . Describe the relationship. (2 points)
Ice cream sales and drownings are correlated. Name a lurking variable. (1 point)

Solutions to check your knowledge

Use these worked steps to check your method before comparing numbers.

Step 1: Q1 - five-number summary

Order the data: $4, 6, 7, 7, 9, 12, 15$ . The minimum is the first value and the maximum is the last. The median is the 4th of 7 values. Split into lower half $4, 6, 7$ and upper half $9, 12, 15$ to find the quartiles.

Answer: Min $4$ , Q1 $6$ , Median $7$ , Q3 $12$ , Max $15$ .

Step 2: Q2 - best display for grouped intervals

A dot plot shows individual values; a box plot shows the five-number summary. Only a histogram bins data into equal-width intervals and displays the frequency of each bin, making it the best choice for showing overall shape in a larger data set.

Answer: A histogram.

Step 3: Q3 - mean and median with an outlier

Add the five values: $3 + 5 + 7 + 9 + 26 = 50$ . Divide by 5 for the mean. For the median, the middle of the ordered list of 5 values is the 3rd value.

Answer: Mean $\dfrac{50}{5} = 10$ ; Median $= 7$ . The outlier $26$ pulls the mean up but leaves the median unchanged.

Step 4: Q4 - resistant measure of center

The mean uses every value's size, so a large outlier pulls it significantly. The median depends only on position in the ordered list, so a single extreme value barely moves it.

Answer: The median.

Step 5: Q5 - joint relative frequency

A joint relative frequency divides a single cell by the grand total of all students, because it asks "what fraction of everyone" falls in that cell.

Answer: $\dfrac{30}{100} = 0.30$ .

Step 6: Q6 - conditional relative frequency

A conditional relative frequency restricts to one group and divides by that group's total, answering "what fraction of juniors prefer pizza" rather than "what fraction of everyone."

Answer: $\dfrac{30}{40} = 0.75$ .

Step 7: Q7 - interpreting slope

The slope $6$ is the predicted change in the response variable (score) for each one-unit increase in the explanatory variable (hours studied). State it with units and use "associated with" rather than "causes," because a model describes a trend.

Answer: Each additional hour studied is associated with about $6$ more points on the score.

Step 8: Q8 - prediction from the model

Substitute $x = 5$ into the line of best fit $y = 6x + 50$ . The model gives a point estimate; call it a prediction, not a guarantee.

Answer: $y = 6(5) + 50 = 30 + 50 = 80$ points.

Step 9: Q9 - interpreting the correlation coefficient

The sign of $r$ gives the direction: negative means as one variable increases the other decreases. The magnitude $0.95$ is close to $1$ , indicating the points cluster tightly around the line.

Answer: A strong negative linear relationship.

Step 10: Q10 - lurking variable

Two variables can move together because a third hidden variable drives both, not because one causes the other. Hot weather increases outdoor swimming (raising drowning risk) and also increases ice cream consumption, so temperature is the common cause.

Answer: Hot weather. It raises both ice cream sales and the amount of swimming, which in turn raises drowning counts.

Sources & how we know this

Louisiana Student Standards for Mathematics — Louisiana Department of Education (2025)
LEAP 2025 Assessment Guide for Algebra I — Louisiana Department of Education (2025)