What is Range?

S7-SA3-0074

Grade Level:

Class 12

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

Definition

What is it?

Range is a simple measure of how spread out a set of numbers is. It tells us the difference between the highest (maximum) and lowest (minimum) values in a data set. A larger range means the data is more spread out, while a smaller range means the data points are closer together.

Simple Example

Quick Example

Imagine your cricket team scored runs in 5 matches: 20, 150, 60, 10, 120. The highest score is 150 runs, and the lowest score is 10 runs. The range of scores would be 150 - 10 = 140 runs.

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.

1. First, list all the temperature values: 32, 35, 29, 36, 30, 33, 34.
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2. Identify the highest value in the list. Here, the highest temperature is 36°C.
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3. Identify the lowest value in the list. Here, the lowest temperature is 29°C.
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4. Subtract the lowest value from the highest value. Range = Highest Value - Lowest Value.
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5. Range = 36 - 29.
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6. Range = 7°C.

So, the range of temperatures for the week is 7°C.

Why It Matters

Understanding range helps engineers design better EVs by analyzing battery performance variations or helps doctors understand the spread of patient recovery times in medicine. In FinTech, it's used to assess the risk of stock price fluctuations, guiding investment decisions and helping you become a smart investor or data scientist.

Common Mistakes

MISTAKE: Forgetting to find the true highest and lowest values, especially if the data is not sorted. | CORRECTION: Always scan through ALL the data points carefully to identify the absolute maximum and minimum values before calculating.

MISTAKE: Subtracting values incorrectly, for example, subtracting the second lowest from the second highest. | CORRECTION: Always subtract the SINGLE lowest value from the SINGLE highest value.

MISTAKE: Confusing range with other measures like mean, median, or mode. | CORRECTION: Remember, range only looks at the spread between the two extreme values, not the average or middle value.

Practice Questions

Try It Yourself

QUESTION: What is the range of ages of children attending a dance class: 8, 12, 9, 10, 11, 8, 13? | ANSWER: 5

QUESTION: A mobile phone battery's charge percentage readings over a day were: 95%, 80%, 65%, 40%, 25%, 10%. What is the range of these readings? | ANSWER: 85%

QUESTION: During a science experiment, the weight of different soil samples (in grams) were recorded as: 25.5, 24.8, 26.1, 25.0, 24.9, 26.5. Calculate the range of the soil sample weights. | ANSWER: 1.7 grams

MCQ

Quick Quiz

Which of the following data sets has the largest range?

10, 12, 15, 18

5, 7, 9, 11

20, 21, 22, 23

1, 5, 10, 20

The Correct Answer Is:

For A, range is 18-10=8. For B, range is 11-5=6. For C, range is 23-20=3. For D, range is 20-1=19. Option D has the largest range.

Real World Connection

In the Real World

In climate science, scientists use range to understand the variation in rainfall or temperature across different regions in India, like comparing the range of monsoon rainfall in Rajasthan versus Kerala. This helps predict weather patterns and manage resources. Even ISRO engineers use range to analyze variations in sensor readings from satellites.

Key Vocabulary

Key Terms

MAXIMUM: The highest value in a data set | MINIMUM: The lowest value in a data set | DATA SET: A collection of numbers or information | VARIATION: The extent to which something differs from others or from a standard

What's Next

What to Learn Next

Great job learning about Range! Next, you should explore 'Mean, Median, and Mode'. These concepts also describe data but in different ways, helping you get an even clearer picture of any set of numbers.