What is Range (Dispersion)?

S7-SA3-0432

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 the simplest measure of dispersion, telling us how spread out a set of data is. It is calculated by finding the difference between the highest and lowest values in a dataset. A larger range means the data points are more spread out, while a smaller range means they are closer together.

Simple Example

Quick Example

Imagine your friend scored 90, 85, 92, 88, and 95 marks in five subjects. The highest mark is 95 and the lowest is 85. The range of their marks would be 95 - 85 = 10. This 10 tells you how much their marks vary.

Worked Example

Step-by-Step

Let's find the range for the daily number of samosas sold at a shop over a week: 120, 155, 130, 145, 160, 110, 135.

Step 1: Identify all the values in the dataset.
Values: 120, 155, 130, 145, 160, 110, 135
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Step 2: Find the highest value in the dataset.
The highest value is 160.
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Step 3: Find the lowest value in the dataset.
The lowest value is 110.
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Step 4: Subtract the lowest value from the highest value.
Range = Highest Value - Lowest Value
Range = 160 - 110
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Step 5: Calculate the result.
Range = 50

Answer: The range of samosas sold is 50.

Why It Matters

Understanding range helps scientists in Climate Science analyze temperature variations or engineers in EV manufacturing check battery performance consistency. It's also crucial for FinTech experts to assess stock price volatility, helping them make smarter investment decisions. Knowing the range gives a quick snapshot of variability, impacting many real-world careers.

Common Mistakes

MISTAKE: Forgetting to find the absolute difference and sometimes getting a negative range. | CORRECTION: Always subtract the lowest value from the highest value, ensuring the range is always a non-negative number.

MISTAKE: Confusing range with other measures like mean or median. | CORRECTION: Range specifically measures the spread (difference between max and min), while mean is the average and median is the middle value.

MISTAKE: Not sorting the data first, leading to errors in identifying the true highest and lowest values, especially in larger datasets. | CORRECTION: It's good practice to sort the data in ascending or descending order before picking out the highest and lowest values to avoid mistakes.

Practice Questions

Try It Yourself

QUESTION: What is the range of ages of children in a tuition class: 8, 12, 10, 9, 11, 10? | ANSWER: 4

QUESTION: A mobile phone battery lasts for these hours on different days: 18, 22, 19, 25, 20, 21. What is the range of battery life? | ANSWER: 7 hours

QUESTION: The temperatures in Delhi over five days were 35°C, 39°C, 32°C, 41°C, 38°C. If the temperature on the sixth day was 30°C, how does the range change? | ANSWER: The original range was 41 - 32 = 9°C. With 30°C, the new lowest is 30°C and highest is 41°C. So, the new range is 41 - 30 = 11°C. The range increased by 2°C.

MCQ

Quick Quiz

Which of the following describes the range of a dataset?

The average of all values

The middle value when data is sorted

The difference between the highest and lowest values

The most frequent value

The Correct Answer Is:

Range is defined as the difference between the highest and lowest values in a dataset, which measures its spread. Options A, B, and D describe mean, median, and mode, respectively.

Real World Connection

In the Real World

In cricket, commentators often talk about the 'range of scores' a batsman has made in recent matches to show their consistency or inconsistency. For instance, if a batsman scores 10, 150, 20, 5, 120, their high range shows they can be unpredictable. This helps team analysts and coaches understand player performance.

Key Vocabulary

Key Terms

Dispersion: How spread out data points are from each other | Highest Value: The maximum number in a dataset | Lowest Value: The minimum number in a dataset | Dataset: A collection of related information or numbers | Variability: The extent to which data points differ from each other

What's Next

What to Learn Next

Now that you understand range, you're ready to explore other important measures of dispersion like Variance and Standard Deviation. These concepts build on range to give a more detailed picture of data spread, which is super useful in data analysis!