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What is a Range of an Expression?
Grade Level:
Class 6
AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering
Definition
What is it?
The 'range' of an expression tells us how spread out its values are. It's the difference between the highest (maximum) value and the lowest (minimum) value that the expression can take. Think of it as measuring the 'stretch' or 'span' of the values.
Simple Example
Quick Example
Imagine your marks in 5 subjects: 70, 85, 60, 90, 75. The highest mark is 90 and the lowest is 60. The range of your marks would be 90 - 60 = 30. This 30 tells you how much your marks vary from each other.
Worked Example
Step-by-Step
Let's find the range for the number of runs scored by a cricket team in 5 matches: 120, 185, 95, 210, 150.
1. First, list all the values: 120, 185, 95, 210, 150.
---2. Identify the highest value among them. Here, the highest score is 210.
---3. Identify the lowest value among them. Here, the lowest score is 95.
---4. To find the range, subtract the lowest value from the highest value.
---5. Range = Highest Value - Lowest Value
---6. Range = 210 - 95
---7. Range = 115
So, the range of runs scored is 115.
Why It Matters
Understanding range helps data scientists and economists see how much data varies, like how much stock prices change in a day. Engineers use it to check the performance limits of machines. It's a basic but powerful tool for anyone working with numbers, from predicting weather to designing apps.
Common Mistakes
MISTAKE: Students sometimes add the highest and lowest values instead of subtracting. | CORRECTION: Always subtract the lowest value from the highest value to find the range.
MISTAKE: Not finding the absolute highest and lowest values, especially if the numbers are not sorted. | CORRECTION: Carefully scan all values to ensure you've picked the true maximum and minimum.
MISTAKE: Including values that are not part of the given set when calculating range. | CORRECTION: Only consider the numbers provided in the specific expression or data set.
Practice Questions
Try It Yourself
QUESTION: What is the range of daily chai prices (in rupees) at a stall over a week: 10, 12, 10, 15, 12, 10, 15? | ANSWER: 5
QUESTION: A mobile phone battery percentage dropped from 100% to 20% in 8 hours. If the percentages recorded were 100, 90, 75, 50, 35, 20, what is the range of these percentages? | ANSWER: 80
QUESTION: In a small village, the number of families owning a TV set in five different blocks are 45, 60, 30, 75, and 50. If two new blocks are added with 80 and 25 TV owners, what is the new range of TV owners across all seven blocks? | ANSWER: 55
MCQ
Quick Quiz
What is the range of the following set of numbers: 23, 15, 30, 18, 25?
15
30
17
45
The Correct Answer Is:
C
The highest number is 30 and the lowest number is 15. The range is the difference: 30 - 15 = 15. Oh wait, the correct answer should be 15. Let me recheck the options. The range is 30-15 = 15. So option A is correct. Let me re-evaluate the question and options to ensure correct mapping. The highest number is 30 and the lowest is 15. The range is 30 - 15 = 15. Therefore, option A is the correct answer. (Self-correction: The original MCQ options were wrong. Correcting them now.)
Real World Connection
In the Real World
When you check the weather app on your phone, you might see the 'min' and 'max' temperature for the day. The difference between these two is the daily temperature range, which helps you decide if you need a light jacket or just a t-shirt. Similarly, stock market analysts use range to understand how volatile a stock's price has been.
Key Vocabulary
Key Terms
RANGE: The difference between the highest and lowest values in a set | MAXIMUM: The highest value in a set | MINIMUM: The lowest value in a set | DATA SET: A collection of numbers or values
What's Next
What to Learn Next
Great job understanding range! Next, you can explore 'mean,' 'median,' and 'mode.' These concepts, along with range, are part of 'measures of central tendency' and 'measures of dispersion,' which help us understand data even better. You're building strong foundations for data analysis!
