Builds on basic graphing to introduce histograms, dot plots, and box plots for displaying distributions of numerical data. Students calculate and interpret mean, median, mode, range, interquartile range (IQR), and mean absolute deviation (MAD), choosing appropriate measures for symmetric versus skewed distributions.
Middle School Geometry & Data • 6-8
Data is everywhere—test scores, temperatures, game statistics, survey results. But a list of numbers by itself is hard to interpret. This lesson teaches you how to organize data visually and calculate numbers that describe what is "typical" and how spread out the data is.
| Display | Best For | Key Feature |
|---|---|---|
| Dot Plot | Small data sets, seeing individual values | A dot above a number line for each data point; clusters and gaps are visible |
| Histogram | Larger data sets, grouped intervals | Bars show frequency of data in ranges (bins); no gaps between bars |
| Box Plot (Box-and-Whisker) | Comparing distributions, showing spread | Shows minimum, Q1, median, Q3, maximum; the box spans the middle 50% |
| Measure | How to Find It | When to Use |
|---|---|---|
| Mean | Add all values, divide by the count | When data is symmetric with no extreme outliers |
| Median | Middle value when data is ordered | When data is skewed or has outliers |
| Mode | Most frequently occurring value | When you want the most common response |
| Measure | How to Find It |
|---|---|
| Range | Maximum − Minimum |
| IQR (Interquartile Range) | Q3 − Q1 (spread of the middle 50%) |
| MAD (Mean Absolute Deviation) | Average distance of each data point from the mean |
In a symmetric distribution, the mean and median are close together and the data looks balanced. In a skewed distribution, a tail stretches to one side. Skewed right = tail goes right (mean pulled higher than median). Skewed left = tail goes left (mean pulled lower than median). Use the median for skewed data.
An outlier is a data point far from the rest. Outliers strongly affect the mean and range but have little effect on the median and IQR. This is why the median is often preferred for skewed data.
Test scores: 78, 85, 90, 85, 92, 88, 85.
Data: 3, 5, 7, 8, 10, 12, 15.
Salaries (in thousands): 40, 42, 45, 47, 50, 200. Compare mean and median.
Students forget to order the data before finding the median. The median is the middle of the sorted list, not the middle of the original list. Always sort first.
1. Find the mean, median, and mode: 12, 15, 18, 15, 20, 15, 22.
Ordered: 12, 15, 15, 15, 18, 20, 22. Mean = 117/7 ≈ 16.7. Median = 15 (4th value). Mode = 15.
2. Data: 4, 6, 8, 10, 12, 14, 16, 18, 20. Find the IQR.
Median = 12 (5th value). Lower half: 4, 6, 8, 10 → Q1 = (6 + 8)/2 = 7. Upper half: 14, 16, 18, 20 → Q3 = (16 + 18)/2 = 17. IQR = 17 − 7 = 10.
3. Scores: 70, 75, 80, 85, 90. Add an outlier of 10. Does the mean or median change more?
Original mean = 80, median = 80. New data (sorted): 10, 70, 75, 80, 85, 90. New mean = 410/6 ≈ 68.3, new median = (75 + 80)/2 = 77.5. The mean dropped by 11.7; the median only dropped by 2.5. The mean changed more.
4. A histogram shows bins 0–10, 10–20, 20–30 with frequencies 2, 8, 5. Which bin contains the median?
Total data points = 2 + 8 + 5 = 15. Median is the 8th value. First bin has values 1–2, second bin has values 3–10. The 8th value falls in the 10–20 bin.
5. Would you use mean or median to describe the typical home price in a neighborhood where most homes cost around $300,000 but one mansion sold for $5,000,000? Explain.
Use the median. The $5,000,000 mansion is an extreme outlier that would pull the mean far above the typical price. The median is resistant to outliers and better represents the typical home.