What is The Range of Data (Max-Min)?

S1-SA4-0386

Grade Level:

Class 3

All STEM domains, Finance, Economics, Data Science, AI, Physics, Chemistry

Definition

What is it?

The Range of Data is the difference between the highest (maximum) and the lowest (minimum) values in a set of numbers. It tells us how spread out the data is, from one end to the other.

Simple Example

Quick Example

Imagine your cricket team scored these runs in 5 matches: 25, 40, 15, 30, 35. The highest score is 40 runs and the lowest score is 15 runs. The range would be 40 - 15 = 25 runs.

Worked Example

Step-by-Step

Let's find the range for the number of samosas sold at a shop each day for a week: 120, 150, 100, 130, 180, 110, 140.

1. First, list all the numbers: 120, 150, 100, 130, 180, 110, 140.
---2. Identify the highest number (maximum value) in the list. Here, the highest number is 180.
---3. Identify the lowest number (minimum value) in the list. Here, the lowest number is 100.
---4. Subtract the lowest number from the highest number: Range = Maximum - Minimum.
---5. So, Range = 180 - 100.
---6. Calculate the difference: 180 - 100 = 80.

The Range of samosas sold is 80.

Why It Matters

Understanding range helps us quickly see how much variation there is in data, which is useful in many fields. Data scientists use it to understand datasets, economists use it to study price changes, and engineers use it to check performance limits in their designs.

Common Mistakes

MISTAKE: Adding the maximum and minimum values instead of subtracting. | CORRECTION: Always subtract the minimum value from the maximum value to find the range.

MISTAKE: Forgetting to find the true maximum or minimum when the data is not sorted. | CORRECTION: Always scan through ALL numbers in the data set carefully to correctly identify the absolute highest and lowest values.

MISTAKE: Confusing range with other statistical measures like average (mean). | CORRECTION: Range specifically measures the spread (difference between max and min), not the central value or typical value.

Practice Questions

Try It Yourself

QUESTION: What is the range of marks scored by students: 75, 88, 62, 91, 70? | ANSWER: 29

QUESTION: A delivery driver recorded these distances (in km) for 5 deliveries: 12.5, 8.0, 15.2, 9.7, 11.0. Find the range of distances. | ANSWER: 7.2 km

QUESTION: The daily temperature in a city for a week was: 28°C, 31°C, 29°C, 30°C, 32°C, 27°C, 30°C. If the next day's temperature was 25°C, how would the range change? | ANSWER: The original range is 32 - 27 = 5°C. With 25°C, the new minimum is 25°C. The new range is 32 - 25 = 7°C. The range increases by 2°C.

MCQ

Quick Quiz

A list of mobile data used by students in a day (in MB) is: 500, 750, 300, 600, 800. What is the range of data usage?

300 MB

500 MB

800 MB

1100 MB

The Correct Answer Is:

The maximum value is 800 MB and the minimum value is 300 MB. The range is 800 - 300 = 500 MB. Options A, C, and D are incorrect as they do not represent the difference between the highest and lowest values.

Real World Connection

In the Real World

In meteorology, understanding the range of daily temperatures helps farmers plan their crops or helps people decide what clothes to wear. For example, knowing the temperature range in Delhi during summer (e.g., 30°C to 45°C) tells you it's very hot and there's a big difference between morning and afternoon temperatures.

Key Vocabulary

Key Terms

Range: The difference between the highest and lowest values in a dataset | Maximum: The largest or highest value in a set of numbers | Minimum: The smallest or lowest value in a set of numbers | Data: A collection of facts, such as numbers or words | Spread: How much the values in a dataset are dispersed or varied

What's Next

What to Learn Next

Great job learning about the Range! Next, you can explore other ways to understand data, like 'Mean, Median, and Mode'. These concepts also help describe data and are very useful in everyday life, building on your understanding of how to analyze numbers.