Box Plots & Histograms: Standardized Test Scores Across Groups Vocabulary Review Sheet

How to Use

• Review each definition and example before your quiz.
• Connect math vocabulary to real-world fairness in education.
• Keep this page in your Equity in Numbers Student Journal.
• Remember: Graphs don’t just show data — they reveal patterns of opportunity.

Histogram

• Definition: A bar graph showing how many data values fall into different ranges (bins).
• Math Example: For scores 50–95 with bins of 10 → bars for 50–59, 60–69, 70–79, etc.
• Real-Life Example: Showing how many students scored in each range on a standardized test.
• Fairness Example: If one group’s bars cluster lower, it may show fewer opportunities, not lower ability.

Bin (Interval)

• Definition: The range of values grouped together in a histogram.
• Math Example: 50–59, 60–69, 70–79.
• Real-Life Example: Grouping student scores to make patterns visible.
• Fairness Example: Using consistent bin widths ensures comparisons between groups are fair and accurate.

Box Plot (Box-and-Whisker Plot)

• Definition: A graph showing the minimum, Q1, median, Q3, and maximum of a data set.
• Math Example: Min = 50, Q1 = 61.25, Median = 72.5, Q3 = 83.75, Max = 95.
• Real-Life Example: Comparing how student test scores spread across schools or groups.
• Fairness Example: Overlapping boxes mean outcomes are similar; separated boxes may show inequities.

Five-Number Summary

• Definition: The five key values that describe a data set → Minimum, Q1, Median, Q3, Maximum.
• Math Example: (50, 61.25, 72.5, 83.75, 95).
• Real-Life Example: Used to create box plots showing score ranges.
• Fairness Example: Helps identify if one group’s test scores are consistently lower than others.

Median

• Definition: The middle number when data is ordered from least to greatest.
• Math Example: 50, 55, 60, 65, 70 → Median = 60.
• Real-Life Example: The typical test score for a group.
• Fairness Example: Median shows a “typical” experience, free from extremes that can distort averages.

Quartile

• Definition: Values that divide a data set into four equal parts (Q1, Q2 = median, Q3).
• Math Example: Q1 = 61.25, Q3 = 83.75.
• Real-Life Example: Used to see where most scores fall in a group.
• Fairness Example: Quartiles show how evenly learning opportunities are distributed.

Interquartile Range (IQR)

• Definition: The range between Q3 and Q1 → shows where the middle 50% of data lies.
• Formula: IQR = Q3 − Q1
• Math Example: Q3 = 83.75, Q1 = 61.25 → IQR = 22.5.
• Real-Life Example: A wide IQR shows varied performance among students.
• Fairness Example: A wider IQR might mean inconsistent support or unequal resources.

Outlier

• Definition: A value much higher or lower than the rest of the data.
• Rule: Outside 1.5 × IQR from Q1 or Q3.
• Math Example: If IQR = 16 and Q3 = 78 → any score above 102 or below 44 is an outlier.
• Real-Life Example: A single very low score might reflect a missing test or barrier to access.
• Fairness Example: Outliers help identify when a student or group’s situation needs special attention.

Distribution

• Definition: The way data values are spread out or grouped.
• Math Example: Histogram shape can be symmetric, skewed left, or skewed right.
• Real-Life Example: Test scores may cluster around 70–80 or spread unevenly.
• Fairness Example: Uneven distributions show where achievement gaps exist.

Skewed Data

• Definition: Data that leans more toward one side of the scale.
• Math Example: Scores 50–70 more frequent than 80–100 → skewed right.
• Real-Life Example: Most students scoring lower can indicate systemic barriers.
• Fairness Example: Skewed data can reflect inequity in preparation or access.

Equity Gap

• Definition: The difference in performance between groups due to unequal opportunity.
• Math Example: Median score for Group A = 74; Group B = 69 → Gap = 5 points.
• Real-Life Example: Comparing test outcomes between different student populations.
• Fairness Example: Closing the equity gap means ensuring all students have resources to succeed.

Interpretation

• Definition: Explaining what the data means in context.
• Math Example: “Group A’s higher median and smaller IQR mean their scores are higher and more consistent.”
• Real-Life Example: Turning graphs into insights about schools and learning conditions.
• Fairness Example: Interpretation connects math results to real change for educational justice.

Summary of Math + Fairness Connections

Concept	Math Focus	Fairness Connection
Histogram	Frequency of data	Reveals score patterns across groups
Box Plot	Medians & quartiles	Highlights opportunity gaps
IQR	Spread of middle 50%	Shows score consistency
Outlier	Extreme values	Identifies areas needing support
Equity Gap	Median differences	Measures fairness in results