What is Range (Statistics)?

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Grade Level:

Class 12

AI/ML, Physics, Biotechnology, FinTech, EVs, Space Technology, Climate Science, Blockchain, Medicine, Engineering, Law, Economics

Definition

What is it?

Range in statistics is a simple measure of how spread out a set of numbers is. It tells you the difference between the highest and the lowest values in a data set. Think of it as the 'stretch' of your data.

Simple Example

Quick Example

Imagine your class had a surprise test, and the marks were 10, 15, 8, 12, 18. The highest mark is 18 and the lowest is 8. The Range would be 18 - 8 = 10. This means the marks are spread across 10 points.

Worked Example

Step-by-Step

Let's find the Range for the daily temperatures in Delhi for a week: 32°C, 35°C, 29°C, 36°C, 30°C, 33°C, 34°C.

Step 1: Identify all the numbers in the data set.
Data: 32, 35, 29, 36, 30, 33, 34

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Step 2: Find the highest value in the data set.
Highest value = 36

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Step 3: Find the lowest value in the data set.
Lowest value = 29

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Step 4: Subtract the lowest value from the highest value.
Range = Highest Value - Lowest Value
Range = 36 - 29

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Step 5: Calculate the result.
Range = 7

Answer: The Range of temperatures for the week is 7°C.

Why It Matters

Understanding Range helps scientists, engineers, and economists quickly grasp how much variation exists in data. For example, in medicine, doctors use range to check if a patient's blood pressure is stable. In finance, it helps predict how much a stock price might change, which is crucial for careers in FinTech.

Common Mistakes

MISTAKE: Forgetting to find the true highest and lowest values, especially in a long list of numbers. | CORRECTION: Always sort the numbers in ascending or descending order first to easily pick out the minimum and maximum.

MISTAKE: Adding the highest and lowest values instead of subtracting them. | CORRECTION: Remember, Range measures the 'difference' or 'spread', so it's always subtraction: Highest - Lowest.

MISTAKE: Including units in the calculation (e.g., 36°C - 29°C = 7°C) and getting confused. | CORRECTION: Perform the subtraction with just the numbers, then add the unit back to the final answer if the data has units.

Practice Questions

Try It Yourself

QUESTION: What is the Range of the following cricket scores: 45, 120, 8, 72, 90? | ANSWER: 112

QUESTION: A mobile phone battery charges to 100%. Over 5 days, its charge levels before plugging in were: 23%, 15%, 30%, 18%, 25%. What is the Range of these battery levels? | ANSWER: 15%

QUESTION: The prices of a 1kg packet of rice at five different kirana stores in your neighbourhood are Rs 65, Rs 72, Rs 68, Rs 80, Rs 60. Later, a new store opens selling it for Rs 55. How does the Range change? | ANSWER: Initially, Range = 80 - 60 = 20. With the new store, Range = 80 - 55 = 25. The Range increases by Rs 5.

MCQ

Quick Quiz

Which of the following describes the Range of a data set?

The average of all values

The middle value when sorted

The difference between the highest and lowest values

The value that appears most often

The Correct Answer Is:

Range is specifically defined as the difference between the maximum (highest) and minimum (lowest) values in a data set. Options A, B, and D describe Mean, Median, and Mode, respectively, which are other statistical measures.

Real World Connection

In the Real World

Farmers in India use Range to understand crop yield variations. If a farmer tracks the kilograms of tomatoes harvested from different plots, calculating the Range helps them see the difference between the most productive and least productive plots. This can help them decide which plots need more attention or different farming techniques to improve overall yield.

Key Vocabulary

Key Terms

DATA SET: A collection of numbers or information | HIGHEST VALUE: The largest number in a data set | LOWEST VALUE: The smallest number in a data set | VARIATION: How much numbers in a set differ from each other | MEASURE OF DISPERSION: A statistic that describes how spread out the values in a data set are

What's Next

What to Learn Next

Great job learning about Range! Next, explore 'Mean', 'Median', and 'Mode'. These are other important ways to understand your data, and together with Range, they give you a much clearer picture of any set of numbers, whether it's cricket scores or climate data.