Range of Data
If the lowest temperature in a city during winter is 5°C and the highest is 25°C, the temperature varies by 20°C. This difference between the highest and lowest values is called the range.
The range tells you how spread out or scattered the data is. A large range means the data is widely spread. A small range means the data is closely grouped together.
In Class 7 NCERT Maths, the range is the simplest measure of the spread of data.
What is Range of Data - Grade 7 Maths (Data Handling)?
Definition: The range of a data set is the difference between the maximum (largest) value and the minimum (smallest) value.
Range of Data Formula
Formula:
Range = Maximum value − Minimum value
Where:
- Maximum value = the largest observation in the data set
- Minimum value = the smallest observation in the data set
Types and Properties
What the range tells you:
- Large range: The data values are widely spread out. For example, test scores of 15, 45, 72, 98 have range = 98 − 15 = 83. The scores vary a lot.
- Small range: The data values are close together. For example, test scores of 70, 72, 75, 78 have range = 78 − 70 = 8. The scores are fairly uniform.
- Zero range: All values are the same. For example, 5, 5, 5, 5 has range = 5 − 5 = 0.
Limitation: The range only uses two values (the maximum and minimum). It does not tell you anything about how the values in between are distributed.
Solved Examples
Example 1: Range of Test Marks
Problem: The marks of 6 students are: 52, 78, 45, 91, 67, 83. Find the range.
Solution:
Step 1: Maximum value = 91
Step 2: Minimum value = 45
Step 3: Range = 91 − 45 = 46
Answer: The range is 46.
Example 2: Range of Temperatures
Problem: Daily temperatures for a week: 28°C, 32°C, 30°C, 35°C, 27°C, 33°C, 29°C. Find the range.
Solution:
Step 1: Maximum = 35°C, Minimum = 27°C
Step 2: Range = 35 − 27 = 8°C
Answer: The range of temperatures is 8°C.
Example 3: Comparing Ranges of Two Data Sets
Problem: Set A: 10, 12, 14, 16, 18. Set B: 5, 12, 14, 16, 30. Which data set has a larger range?
Solution:
Range of A = 18 − 10 = 8
Range of B = 30 − 5 = 25
Answer: Set B has a larger range (25) compared to Set A (8). Set B's data is more spread out.
Example 4: Range of Cricket Runs
Problem: A batsman's scores in 5 matches: 0, 45, 23, 110, 67. Find the range.
Solution:
Maximum = 110, Minimum = 0
Range = 110 − 0 = 110
Answer: The range is 110 runs. This shows the batsman's scores varied a lot.
Example 5: Range with Negative Numbers
Problem: Temperatures in a hill station over 5 days: −3°C, 2°C, −1°C, 5°C, 0°C. Find the range.
Solution:
Maximum = 5°C, Minimum = −3°C
Range = 5 − (−3) = 5 + 3 = 8°C
Answer: The range is 8°C.
Example 6: Range of Heights
Problem: Heights of 5 students (in cm): 148, 155, 142, 160, 150. Find the range.
Solution:
Maximum = 160 cm, Minimum = 142 cm
Range = 160 − 142 = 18 cm
Answer: The range of heights is 18 cm.
Example 7: Range When All Values Are Equal
Problem: Find the range of: 25, 25, 25, 25.
Solution:
Maximum = 25, Minimum = 25
Range = 25 − 25 = 0
Answer: The range is 0. All values are the same, so there is no spread.
Example 8: Word Problem on Range
Problem: The prices of 6 books are: Rs. 120, Rs. 85, Rs. 200, Rs. 150, Rs. 95, Rs. 175. Find the range of prices.
Solution:
Maximum = Rs. 200, Minimum = Rs. 85
Range = 200 − 85 = Rs. 115
Answer: The range of book prices is Rs. 115.
Real-World Applications
Real-life uses of the range:
- Weather: Meteorologists report the range of temperatures to show how much the weather varies in a day or season.
- Quality control: In factories, the range of product measurements shows consistency. A small range means products are uniform.
- Sports: The range of scores shows how consistent a player is. A small range means steady performance.
- Stock market: The range of stock prices over a day or week shows how volatile a stock is.
- Exams: Teachers check the range of marks to see how varied student performance is.
Key Points to Remember
- Range = Maximum value − Minimum value.
- The range measures the spread of data.
- A large range means data is widely spread; a small range means data is closely grouped.
- If all values are the same, the range is 0.
- The range only uses the two extreme values and ignores everything in between.
- The range is easy to calculate but can be misleading if there is one outlier.
- The range is always a non-negative number (zero or positive).
Practice Problems
- Find the range of: 15, 22, 8, 30, 17.
- The weights of 5 parcels are: 2.5 kg, 4.8 kg, 1.2 kg, 3.6 kg, 5.0 kg. Find the range.
- Temperatures recorded: −5°C, 3°C, −2°C, 7°C, 1°C. Find the range.
- Two students' marks over 5 tests: Student A: 70, 72, 68, 75, 71. Student B: 50, 90, 65, 80, 55. Find the range for each. Who is more consistent?
- If the range of a data set is 0, what does it tell you about the data?
- The range of 5 observations is 18. If the minimum value is 7, what is the maximum value?
Frequently Asked Questions
Q1. What is the range of a data set?
The range is the difference between the largest value and the smallest value in a data set. Range = Maximum − Minimum.
Q2. Can the range be negative?
No. Since the maximum is always greater than or equal to the minimum, the range is always zero or positive.
Q3. What does a range of 0 mean?
A range of 0 means all the values in the data set are the same. There is no variation.
Q4. Is the range a good measure of spread?
The range is simple and quick to calculate, but it has limitations. It only uses two values and can be greatly affected by one outlier. Other measures like the interquartile range give a better picture of spread.
Q5. How is range different from mean?
The mean measures the central value (average) of data. The range measures the spread of data (how far apart the highest and lowest values are). They describe different aspects of the data.
Q6. Can the range be a decimal?
Yes. If the data values are decimals, the range can also be a decimal. For example, the range of 2.5 and 4.8 is 4.8 − 2.5 = 2.3.
