Topic 1.1: Introducing Statistics: What Can We Learn from Data?
What Can We Learn from Data? Identifying Questions in Context and Using One-Variable Data
Video Follow-Along Worksheet
↻ Already did this one? It stays open even after it’s checked off — just change any answer and click ✓ Check Answers again (no need to Reset). ✨ Grade with AI only ever raises your grade. Make sure you’re signed in so your changes save.
Learning Objectives:
Identify the question to be answered or problem to be solved in a given context.
Recognize how statistics can help answer important real-world questions based on data that vary.
Identify questions to be answered based on variation in one-variable data.
Explain why numbers become meaningful when they are placed in context.
Use a real data example to connect a question, a variable, and an interpretation.
Essential Knowledge:
Variation means data values are not all the same, so conclusions can be uncertain.
In Topic 1.1, we focus on identifying the statistical question before trying to answer it.
Numbers may convey meaningful information when placed in context.
One-variable data involve values of a single variable, such as lead level in water.
Statistics can help answer questions by collecting data, analyzing data, and interpreting results.
Key Vocabulary
Statistics
The science of learning from data.
Context
The real-world setting that gives numbers meaning.
Variable
A characteristic measured on each individual in a study.
One-Variable Data
Data that record values for a single variable.
Variation
Differences in data values from one observation to another.
Sample
The group from which data are collected.
Lead Level
The amount of lead in a water sample, measured in parts per billion.
Threshold
A cutoff used to decide whether action should be taken.
Analyze Data
Examine the data to look for patterns and answer questions.
Interpret Results
Explain what the results mean in the original situation.
Video 1: Introducing Statistics with the Flint Water Crisis
[0:00 – 6:40]
1.[0:25]
One goal of the video is to identify the statistical to be answered or the to be solved in a given .
2.[0:34]
Statistics can help answer important real-world questions based on data that .
Flint Water Crisis[0:47 – 1:35]
In Flint, Michigan, the city switched its water supply in April 2014 from Lake Huron to the Flint River to save money. Residents complained that the water looked, smelled, and tasted bad, while city officials claimed that the water was safe to drink.
3.[0:52]
The example in this lesson is the Flint water in Flint, .
4.[1:05]
In April 2014, the city switched its water supply from Lake to the Flint to save .
5.[1:18]
Residents said the water looked, smelled, and tasted .
6.[1:42]
The central question was whether Flint's water was safe to .
7.[1:50]
City officials measured levels in water samples collected between and 2015.
8.[2:01]
The data ranged from parts per billion to parts per billion.
9.[2:10]
Lead levels greater than parts per billion are considered extremely .
Flint Safety Rule[2:35]
If more than 10% of water samples have lead levels greater than 15 parts per billion, the water is deemed not safe to drink.
The key question is tied to one variable: lead level in a water sample.
10.[2:54]
In this example, the one-variable data are the lead levels measured in parts per .
11.[3:00]
An important question was: what of the 71 water samples exceeded 15 parts per billion?
12.[3:18]
From the graph, of the samples were above 15 parts per billion.
13.[3:29]
That proportion is , or .
14.[3:41]
Because 11.3% is greater than the 10% threshold, the water was to drink.
15.[3:48]
City officials omitted water samples, including readings of and parts per billion.
16.[4:40]
After omitting those two samples, out of samples exceeded 15 parts per billion.
17.[4:47]
That is , or , so the city declared the water to drink.
18.[5:13]
Virginia Tech researchers later found that about of samples had lead levels above 15 parts per billion.
What Happened Next?[5:13 – 5:57]
Virginia Tech researchers found lead levels above the action threshold in about 17% of samples. Flint pediatrician Mona Hanna-Attisha also found that elevated blood lead levels in children had doubled since the water-source switch. Courts later required bottled water delivery and replacement of Flint's lead pipes.
19.[6:24]
After you ask questions, you collect data, data, and the results.
Statistics Process[6:24 – 6:34]
Ask a question or identify the problem.
Collect data.
Analyze the data.
Interpret the results in context.
20.
Reflection: Why does a number like 15 parts per billion or 11.3% only become meaningful when it is placed in context?
21.
Reflection: How did removing two water samples change the conclusion, and what does that show about using statistics responsibly?
Exit Ticket
A school health office records the number of hours of sleep the night before a big exam for a random sample of 30 students. The principal wants to know whether too little sleep is a concern for these students. The data show that 9 of the 30 students got fewer than 6 hours of sleep.
(a) Identify the question to be answered or problem to be solved in this context.
(b) Describe the variable and explain what it means for the data to vary.
(c) Explain why the number 9/30 = 30% is only meaningful when placed in context.
(d) Briefly describe how statistics could be used to help answer the principal's question.
Class Responses (Esc to close)
Click a "Class" button next to a question to see responses.