Unit 6: Statistics & Data Analysis
Master the art of statistics and data analysis, learning to collect, organize, and interpret data through various displays and measures
Unit 6 Overview
Unit 6 focuses on understanding and analyzing data through statistical questions. Students learn how to find measures of center (mean, median, mode) and variation (range, IQR), and represent data using dot plots, histograms, and box plots. These skills help students make sense of real-world information and compare different data sets.
You'll learn to identify statistical questions that anticipate variability, calculate measures of center and spread, and create various data displays. You'll also learn to interpret and compare data sets using appropriate statistical measures and visual representations.
Get ready to become a data detective!
Learning Objectives
- Identify statistical questions that anticipate variability
- Calculate measures of center (mean, median, mode) and variation (range, IQR)
- Create and interpret dot plots, histograms, and box plots
- Understand the five-number summary and its relationship to box plots
- Compare and summarize data sets using appropriate statistical measures
Your Progress
Statistical Questions & Data Sets
A statistical question anticipates variability and asks about a population. The Georgia Standards explain that a statistical question "anticipates variability" and that data collected to answer such questions have a distribution described by its center, spread, and overall shape.
For example, "How old am I?" is not a statistical question, but "How old are the students in my school?" is a statistical question.
What You'll Learn:
- Identify statistical questions that anticipate variability
- Distinguish between statistical and non-statistical questions
- Understand how data collection relates to statistical questions
- Recognize the characteristics of good statistical questions
Key Characteristics:
- Anticipates variability in responses
- Asks about a population or group
- Has multiple possible answers
- Requires data collection to answer
Why it matters: helps us understand patterns and make informed decisions based on data.
Khan Academy – Statistical & Non‑Statistical Questions
Learn to identify statistical questions that anticipate variability versus non-statistical questions with clear examples and explanations.
Watch on YouTubeStatistical Questions vs. Non-Statistical Questions
Compare statistical and non-statistical questions with practical examples to understand the key differences and characteristics.
Watch on YouTubeMeasures of Center
Measures of center summarize a set of numerical data with a single number. The framework notes that a measure of center (mean or median) summarizes all values, while a measure of variation describes how the values vary.
Students learn to compute the mean (average), median (middle value) and mode (most frequent value) and to decide which is appropriate depending on the data's distribution.
What You'll Learn:
- Calculate the mean (average) of a data set
- Find the median (middle value) of a data set
- Identify the mode (most frequent value)
- Choose the appropriate measure of center for different data distributions
Math Antics – Mean, Median & Mode
Learn the three main measures of center: mean, median, and mode, with clear explanations and examples.
Watch on YouTubeMath with Mr. J – Finding Mean, Median & Mode
Step-by-step guide to calculating mean, median, and mode with practical examples and clear explanations.
Watch on YouTubeMeasures of Variation
Variation describes how spread out data are. The unit framework teaches that students should determine quantitative measures of variability such as range and interquartile range (IQR).
The range is the difference between the maximum and minimum values, while the IQR (Q3 – Q1) is the "middle 50%" of data in a box plot.
What You'll Learn:
- Calculate the range of a data set
- Find the interquartile range (IQR)
- Understand how variation describes data spread
- Use range and IQR to compare data sets
Math with Mr. J – Interquartile Range (IQR)
Learn how to calculate the interquartile range (IQR) and understand what it tells us about data spread.
Watch on YouTubeKhan Academy – Range and Interquartile Range
Comprehensive explanation of range and IQR with examples showing how to calculate and interpret these measures of variation.
Watch on YouTubeData Displays: Dot Plots & Histograms
Numerical data can be displayed on a number line using dot plots, where each dot represents a data point. Histograms display continuous data using bars (bins) and show frequency distributions.
The unit framework encourages students to create frequency tables leading to histograms and to relate the shape of a histogram to the corresponding dot plot. Students should mark mean and median on histograms and describe shapes as symmetric or skewed.
What You'll Learn:
- Create and interpret dot plots for numerical data
- Build frequency tables and histograms
- Identify symmetric and skewed distributions
- Mark mean and median on data displays
Khan Academy – Dot Plots & Frequency Tables
Learn how to create and interpret dot plots and frequency tables to display numerical data effectively.
Watch on YouTubeKhan Academy – Histograms
Learn how to create and interpret histograms to display continuous data and frequency distributions.
Watch on YouTubeBox Plots & Five-Number Summary
Box plots (also called box‑and‑whisker plots) display the five‑number summary: minimum, lower quartile (Q1), median, upper quartile (Q3) and maximum.
The unit explains that the "box" represents the middle 50% of data and that the length of the box corresponds to the IQR. Students use box plots to compare distributions and discuss outliers and skewness.
What You'll Learn:
- Identify the five-number summary of a data set
- Create and interpret box plots
- Understand how the box represents the middle 50% of data
- Compare distributions using box plots
Math Antics – Box and Whisker Plots
Learn how to create and interpret box plots, including the five-number summary and identifying outliers.
Watch on YouTubeKhan Academy – Constructing a Box and Whisker Plot
Step-by-step guide to creating box plots from data, including finding quartiles and identifying outliers.
Watch on YouTubeSummarizing & Comparing Data Sets
Summarizing data involves reporting the number of observations, describing the attribute and its units, and giving quantitative measures of center (mean or median) and variability (range or IQR).
Students learn to choose appropriate graphs (dot plots, histograms, box plots) and decide whether the mean or median better describes a distribution based on its shape. The essential questions encourage students to compare data sets, decide which graphs best represent data and draw conclusions.
What You'll Learn:
- Summarize data sets using appropriate measures
- Choose the best graph type for different data
- Compare multiple data sets effectively
- Draw meaningful conclusions from data analysis
Khan Academy – Comparing Dot Plots, Histograms & Box Plots
Learn how to compare different data displays and choose the most appropriate graph for your data.
Watch on YouTubeKhan Academy – Impact on Mean & Median When Removing Data
Understand how removing data points affects the mean and median, and learn to choose the best measure of center.
Watch on YouTube