Unit 1 Lesson 6 - Describing Quantitative Distributions

Describing Quantitative Distributions

Unit 1, Topic 1.6: Describing Quantitative Distributions

Overview

This lesson focuses on describing quantitative data (like test scores or heights) by looking at its shape, center, spread, and odd features. Graphs and numbers help us see these patterns. Context—like who the data is from—matters because it explains why shapes or outliers appear. For example, a set of “5 heights” could show a trend for kids or adults without context.

Quantitative data uses numbers to measure amounts (e.g., time, weight). We’ll describe shapes (like symmetric or skewed), find the center (like the middle value), measure spread (like the range), and spot unusual parts (like outliers or gaps). This helps us understand the data without guessing about bigger groups.

Examples:
Skewed left vs skewed right : example
Unimodal, Bomodal graph : example
Uniform Grapgh :

Part 1: Guided Practice Activity

Work on your own. Use the data below from 15 students (from a class survey). Describe its distribution and identify features.

Data:

• Test Scores: 55, 60, 65, 68, 72, 75, 78, 80, 82, 85, 87, 90, 92, 95, 100

Tasks:

1. Describing the Distribution:
   • Describe the shape (e.g., symmetric, skewed right/left, unimodal/bimodal/uniform).
   • Find the center (e.g., estimate the middle value or mean).
   • Note the variability (e.g., range from lowest to highest).
   • Spot unusual features (e.g., outliers, gaps, clusters, peaks).
   • Write 1–2 sentences about variation (e.g., “Scores spread from 55 to 100, with a peak around 80–90.”).
   • Extra Practice: Use your own data (e.g., “Daily Steps: 4000, 4500…” from 5 days). Describe its shape, center, variability, and features.
2. Identifying Outliers:
   • Pick out any outliers (values much smaller or larger than the rest, e.g., more than 1.5 times the range from the middle).
   • Write 1–2 sentences explaining why they stand out (e.g., “55 is an outlier, maybe from a student who missed class.”).
   • Extra Practice: Check your “Daily Steps” data for outliers and explain.
3. Reflection:
   • Write 2–3 sentences about how these descriptions summarize data without guessing about everyone, and why precise words matter. (Example: “This shows most scores are 70–100, but doesn’t prove it for all students. Using ‘skewed right’ clearly notes the low outlier at 55.”)

Part 2: Independent Practice

Look at this data from a survey of 12 students:

• Heights (cm): 140, 145, 150, 152, 155, 158, 160, 165, 168, 170, 175, 185

Tasks:

• Describe the shape, center, variability, and unusual features of the distribution.
• Identify any outliers and explain why they’re unusual.
• Write 2–3 sentences interpreting the distribution in context, justifying a claim (e.g., “The height spread suggests growth, with 185 possibly from an older student.”).
• Extra Activity: Invent a dataset for 10 people (e.g., “Screen Time (hours): 2, 3…”). Describe its distribution, check for outliers, and write why it could suggest a question like “Do teens use screens more at night?”

Homework Assignment

• Collect data from 5 people on a quantitative variable (e.g., minutes spent gaming: 30, 45…). Describe its shape, center, variability, and any unusual features, then explain how context helps interpret it to share next class.