How to Calculate the Range of Data with Step-by-Step Examples
When we get a huge amount of data, we use different statistical terms to describe it. These include mean, mode, median, and range. Before calculating the range of data, it is crucial to understand these statistical terms.
So, let us discuss them more deeply.
Statistics
What is Mean?
Mean is nothing but the average of the numbers or the data given. The formula for getting mean is:
Sum of all the numbers in the data/ number of the numbers
For example: If there are five numbers from 1 to 5, their sum is 15, and the total numbers are 5. So, according to the formula, the mean is 15/5 equal to 3.
Mean
What is Mode?
Mode refers to the number that appears frequently or most of the time in a number series. If two numbers appear most frequently, there will be two modes. Hence, it will be called bimodal. If more than two numbers occur mostly, the data will be called multimodal. If all numbers appear with the same occurring frequency, then there will be no modes.
Mode
What is the Median?
Median is the middle number or a centrally occurring number in a data series. The first step to finding the median is to arrange data from lowest to highest or highest to lowest. If there are an odd number of data points, there will be one middle number as the median. Further, in the case of an even number of data points, there will be two middle numbers, and the median will be calculated by adding those numbers and dividing them by 2.
Median
What is the Range of Data?
In range statistics, the range is defined as the difference between the highest and lowest number in a data set. For example: if there is a data set given (2, 4, 6, 8, 12), the range will be 12 - 2 = 10. Therefore, the range could also be calculated by taking out the difference between the highest and lowest observation. The result is known as the range of the observation. It shows the spread of observation in statistics or data handling.
Range
What is the Range of Data Formula?
The formula to calculate the range of a set relies on the difference between the highest and the lowest values. Here are some of the range formulas.
Range = Highest value- lowest value.
Range = Highest observation- lowest observation.
Range = Maximum value- minimum value.
How to Find the Range of Data?
The first step to begin finding a range involves arranging the given data sets or numbers in ascending order. This means writing the lowest value first and moving on to the highest value at last. Then, use the formula to get the range of the data set.
Examples
Q1. Find the range of the given number series: 30, 25, 20, 35, 15, 40.
Ans: First arrange the numbers in ascending order. The new series will be; 15, 20, 25, 30, 35, and 40. Now, the highest value is 40, and the lowest value is 15. So, we can apply the formula, Range = Highest value - lowest value. Range = 40-15 = 25.
Q2. Find the range of the data series: 5, 9, 7, 11.
Ans: The new series is 5, 7, 9, and 11. The highest number is 11 and the lowest is 5. Hence, the range will be the highest number - lowest number or 11 - 5 = 6.
Q3. What is the range of the given series: 40, 45, 55, 50?
Ans: The new series is 40, 45, 50, and 55. The highest number is 55 and the lowest number is 40. The range is the highest number- lowest number= 15.
Practise Questions
Q1. What is the range of the series: 1, 3, 5, 7?
Ans: 6
Q2. Find the range of 2, 5, 8, and 11.
Ans: 9
Q3. What is the range of 20, 24, 28, and 32?
Ans: 12
Summary
In Mathematics, the mean is the average of the given numbers calculated by adding the numbers and dividing them by total numbers. Mode is the most frequent or repeating number in a data series. The median is the middle number in a given data set. All these terms are accompanied by 'range'. It is the difference between the maximum and minimum numbers or highest and lowest observations.
FAQs on What Is the Range of Data?
1. What is the range of data in statistics?
In statistics, the range is the simplest measure of spread or dispersion within a data set. It is defined as the difference between the highest (maximum) and the lowest (minimum) values in a distribution. A larger range signifies that the data is more spread out, whereas a smaller range indicates that the data points are clustered closely together.
2. What is the formula used to calculate the range of a data set?
The formula to calculate the range is very straightforward. You simply subtract the lowest value from the highest value observed in the data set. The formula is:
Range = Highest Value (Maximum) – Lowest Value (Minimum).
3. What are the steps to find the range of a given set of numbers?
To find the range of a data set, you can follow these simple steps as per the methodology taught in NCERT textbooks:
- Step 1: Collect all the numbers or observations in the data set.
- Step 2: Arrange the data set in ascending order (from smallest to largest) to easily identify the extremes.
- Step 3: Pinpoint the highest value (the last number in the ordered list) and the lowest value (the first number).
- Step 4: Apply the formula by subtracting the lowest value from the highest value to find the range.
4. Can you show how to calculate the range with an example?
Certainly. Let's find the range for the following data set representing the marks of a student in five tests: {25, 48, 19, 50, 32}.
- First, arrange the marks in ascending order: {19, 25, 32, 48, 50}.
- The highest value (maximum mark) is 50.
- The lowest value (minimum mark) is 19.
- Now, use the formula: Range = Highest Value – Lowest Value.
- Range = 50 – 19 = 31.
- Therefore, the range of this data set is 31.
5. What is the main difference between range and mean in data handling?
The primary difference between range and mean is what they describe about a data set:
- The range is a measure of dispersion or spread. It tells you about the variability in the data, showing how far apart the maximum and minimum values are.
- The mean, or average, is a measure of central tendency. It identifies the central point or typical value of the data set.
In short, range describes how spread out the data is, while the mean describes its central location.
6. Why is the range an important, though simple, measure in data analysis?
The range is important because it offers a quick, easy-to-calculate snapshot of the variability within a data set. It provides an immediate sense of how spread out the values are, which is a fundamental first step in data analysis. For instance, in weather reporting, the daily temperature range gives a clear picture of temperature fluctuation. While it's a basic measure, its simplicity makes it highly accessible for a preliminary assessment of data.
7. Does the range give a complete picture of how data is spread?
No, the range provides a limited view of data spread. Its biggest weakness is that it only considers two data points: the highest and lowest values. This makes it highly sensitive to outliers (unusually high or low values) and it completely ignores the distribution of all other data points in between. For a more robust and detailed understanding of data dispersion, statisticians often use other measures like the interquartile range (IQR) and standard deviation.
8. Where might we see the concept of range being used in real life?
The concept of range is frequently used in various real-world contexts to understand variation:
- Weather Forecasting: To describe the daily range of temperatures (difference between high and low).
- Finance & Stocks: To show a stock's price range during a trading day.
- Healthcare: To define the normal or healthy range for metrics like blood pressure or cholesterol levels.
- Manufacturing: In quality control, to ensure that the dimensions or weight of products fall within an acceptable range.
