Measures of Variability

Free sample questions, a clear explanation, and 5 practice skills with an AI tutor that guides without giving the answer away.

Concept Review

Range: How Spread Out Is Your Data?

Imagine you're comparing the heights of players on two basketball teams. Team A has players who are all around 6 feet tall. Team B has some players at 5'2" and others at 6'10". Which team has more variety? The answer lies in understanding range — the spread between the highest and lowest values in your data.

Range is like measuring the wingspan of your data. It tells you how much space your numbers cover from the smallest to the largest value. Think of it as the distance between the two end points on a number line.

Calculating Range: The Simple Formula

Finding range is surprisingly straightforward: Range = Highest Value - Lowest Value

Let's see this in action with those basketball teams:

Team A Heights (in inches): 70, 72, 71, 73, 69

• Highest value: 73 inches

• Lowest value: 69 inches

• Range: 73 - 69 = 4 inches

Team B Heights (in inches): 62, 75, 82, 68, 79

• Highest value: 82 inches

• Lowest value: 62 inches

• Range: 82 - 62 = 20 inches

Team B has a much larger range, confirming what we suspected — their heights are much more spread out!

⚡ Range Reality Check

Here's something that might surprise you: range only cares about two numbers — the highest and lowest values. You could have 100 data points, but range completely ignores the 98 numbers in the middle!

This means two very different data sets can have the exact same range. For example: [1, 2, 3, 4, 5] and [1, 1, 1, 5, 5] both have a range of 4, even though they look completely different.

Range in Real Life

Range shows up everywhere around you:

🌡️ Weather: "Today's temperature range is 45°F to 78°F" (Range = 33°F)
💰 Prices: Restaurant meals from $8 to $25 (Range = letter: 'GG', title: 'Measures of Variability', concept: 7)
📊 Test Scores: Class scores from 67 to 95 (Range = 28 points)

🔑 Key Takeaway

Just like those basketball teams showed us different levels of variety, range gives you instant insight into how consistent or varied your data is. A small range means your data points stick close together — like a tight team. A large range means your data is spread out far and wide — lots of variety, but also less predictability.

Sample questions

1. The range is calculated by:

○ Adding all numbers

✓ Maximum - Minimum

○ Finding the middle

○ Maximum + Minimum

Answer: Maximum - Minimum — Range shows the total span of the data.

2. Find the range: 12, 5, 19, 2, 30.

○ 28

○ 30

✓ 28? 30 - 2 = 28

○ 15

Answer: 28? 30 - 2 = 28 — Max (30) minus Min (2).

3. What does a range of 0 mean?

✓ All numbers in the data set are identical

○ The data set is empty

○ The mean is zero

○ The numbers are all negative

Answer: All numbers in the data set are identical — If there is no difference between max and min, the numbers are the same.

Skills in this topic

Calculate the range of a data set
Understand the concept of deviation from the mean
Calculate the Mean Absolute Deviation (MAD)
Understand the Interquartile Range (IQR) as a measure of variation
Compare the variability of two different data sets

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