In statistics, a range refers to the difference between the highest and lowest values in a dataset. It provides a simple measure of the spread or dispersion of the data. Calculating the range involves subtracting the minimum value from the maximum value.
Range is a fundamental statistical concept that helps us understand the spread or variability of data within a dataset. Range in Statistics provides valuable insights into the extent of variation among the values in a dataset. Range quantifies the difference between the highest and lowest values in the dataset.
Let's discuss in detail about range in statistics with its definition and formula.
What is Range?
Range offers a straightforward measurement of the data's spread or variability. The range statistic is simple and straightforward to calculate, but it has limitations because it only takes into consideration the maximum and minimum values and ignores the distribution of values across the dataset.
Range in statistics is the difference between the highest and lowest values in a dataset.
Range in StatisticsFormula
Below is the range formula of statistics.
Range = Maximum Value - Minimum Value
How to Calculate Range?
We can use following steps for range calculation:
- Identify the maximum value (the largest value) in your dataset.
- Identify the minimum value (the smallest value) in your dataset.
- Subtract the minimum value from the maximum value to find the range.
Range=Maximum value−Minimum value
Here Is An Solved Example To Find Range
Example: Consider the following dataset of exam scores for a class tenth:
77, 89, 92, 64, 78, 95, 82
Find the Range of the above data
Solution:
Now To Calculate the range
Here, Select The Largest Score as Maximum Value and Smallest score as Minimum Value:
Maximum value = 95
Minimum value = 64
Range = 95 - 64 = 31
So, the range of the exam scores in this dataset is 31.
Range in Dataset
The range of a dataset is quite simple to understand. It is the difference between the highest (maximum) and lowest (minimum) values in that dataset. Mathematically, the formula for calculating the range is as follows:
Range = Maximum Value - Minimum Value
This simple formula provides a quick way to quantify the spread of data.
Range for Grouped Data
In Grouped data where the datasets are arranged in Class Intervals, the Range is find by subtracting the lower limit of the first class interval and the upper limit of the last class interval. We can understand it from the example mentioned below:
Class Interval | Frequency |
|---|
0-10 | 12 |
10-20 | 10 |
20-30 | 15 |
30-40 | 13 |
40-50 | 11 |
Range = Upper Limit of the Last Class Interval - Lower Limit of First Class Interval = 50-0 = 50
Range Applications
The applications of range are mentioned below:
- Range has got its application in various fields, such as mathematics, science, economics, and social sciences.
- Range is basically used to analyze the variation and dispersion of a dataset.
- Range is used in educational assessments to understand the variation in scores of Students
- In clinical trials and medical research, the range of outcomes for a particular treatment or medication is studied to determine its effectiveness and potential side effects.
- In sports, range can be applied to analyze player's performance.
Advantages and Disadvantages of Ranges in Statistics
The range in statistics has both advantages and disadvantages:
Advantages
- Easy to understand: The concept of range is simple and easy to grasp for people unfamiliar with statistics. It's essentially the difference between the highest and lowest values in a dataset, making it intuitive.
- Quick to calculate: Computing the range involves only finding the maximum and minimum values in the dataset and subtracting them, making it a fast measure to calculate.
- Provides a basic measure of variability: Despite its simplicity, the range gives a basic indication of the spread or variability of the data. A larger range suggests greater variability, while a smaller range suggests less variability.
Disadvantages
- Sensitivity to outliers: The range is heavily influenced by extreme values (outliers) in the dataset. A single outlier can greatly inflate the range, potentially giving a misleading picture of the variability of the majority of the data.
- Does not consider distribution: The range does not take into account the distribution of values within the dataset. Two datasets with the same range can have very different distributions, leading to different interpretations of variability.
- Limited information: While the range provides a basic measure of variability, it does not provide any information about the distribution's shape or central tendency. Other measures such as the interquartile range, variance, or standard deviation offer more comprehensive insights into the dataset's characteristics.
- Sample size dependency: The range does not account for sample size, so datasets with different sample sizes may have similar ranges even if their variability differs significantly. This can lead to misinterpretations, especially when comparing datasets of different sizes.
Solved Examples on Range
Example 1: You are given a dataset of the ages of students in a classroom:
18, 19, 20, 21, 22, 35, 18, 23
Solution:
Maximum Value = 35
Minimum Value = 18
Range = 35 - 18 = 17
The range of ages among the students is 17 years.
Example 2: Consider a dataset of exam scores for a class:
Scores: 85, 92, 78, 96, 64, 89, 75, find the range?
Solution:
Maximum Value = 96
Minimum Value = 64
Range = 96 - 64 = 32
So, the range of the exam scores is 32.
Example 3: Imagine a dataset of monthly rainfall (in millimeters) for a city for the past year:
Rainfall: 50, 48, 52, 58, 45, 70, 65, 80, 40, 42, 75, 90, find the range of monthly rainfall for the city?
Solution:
Maximum Value = 90
Minimum Value = 40
Range = 90 - 40 = 50
The range of monthly rainfall for the city is 50 mm
Example 4: You are given a dataset of the heights of students in a classroom(in cm): 150, 155, 160, 165, 170, 175. Find Range.
Solution:
Maximum Value = 175 cm
Minimum Value = 150 cm
Range = 175 - 150 = 25 cm
The range of heights of students is 25 cm
Example 5: Consider a dataset of daily temperature of a city( in °F): 68°F, 72°F, 75°F, 70°F, 74°F. Find temperature range.
Solution:
Maximum Value = 75°F
Minimum Value = 68°F
Range = 75 - 68 = 7°F
Hence the temperature range is 7°F
Example 6: Compare and contrast the range with other measures of variability such as variance and standard deviation.
Solution:
- Range: Measures the difference between the maximum and minimum values; it is simple but sensitive to outliers.
- Variance: Measures the average squared deviation of each data point from the mean, providing a more comprehensive understanding of variability, but is more complex to calculate.
- Standard Deviation: The square root of variance, it is also a measure of spread but is in the same units as the data, making it easier to interpret than variance.
Example 7 : Consider the following dataset representing the ages of participants in a survey:
22, 28, 34, 31, 25, 30, 29, 33, 27, 24
Calculate the range of the ages in this dataset.
Solution:
Identify the Maximum Value: The highest age in the dataset is 34.
Identify the Minimum Value: The lowest age in the dataset is 22.
Calculate the Range:
Range = Maximum value − Minimum value
Range=Maximum value−Minimum value = 34−22 = 12
Answer:
The range of the ages in this dataset is 12 years.
Conclusion
Range is a measure of variability in a dataset, it tells the spread between the highest and lowest values of the dataset. The simple understanding and easy method of calculation of range makes it a useful tool in various fields. However, the range has limitations, it is unable to tell about the size or the central tendency of the data which can lead to errors in understanding when comparing datasets of different sizes. For a better understanding of variability we need to consider other measures, such as variance or standard deviation.
Practice Questions On Range In Statistics
Q1. Calculate the range for the following dataset: 12, 15, 20, 25, 30, 35, 40, 45?
Q2. A dataset of temperatures in degrees Celsius for a week is given as follows: 18, 22, 20, 25, 19, 28, 17. Find the range?
Q3. You have a dataset of the heights (in inches) of a group of individuals: 62, 67, 71, 68, 70, 75, 61, 66, 69, 70. Determine the range of heights?
Q.4. Consider the following data for the number of books read by students in a year: 4,9,15,7,12,6. Find the range of the dataset.
Q.5. A survey of 10 people recorded their ages as follows: 25,32,28,45,34,50,29,41,33,36. Calculate the range of the ages.
Q.6. Given the following grouped data, calculate the range:
Class Interval | Frequency |
|---|
0-20 | 8 |
|---|
20-40 | 12 |
|---|
40-60 | 15 |
|---|
60-80 | 10 |
|---|
Q.7. You have the following test scores of 5 students: 85,90,78,92,88. Determine the range of the test scores.
Q.8. A researcher records the temperatures (in °C) of 6 cities on a particular day: 12,15,14,19,21,16. Find the range of temperatures.
Q.9. For the grouped data below, determine the range:
Class Interval | Frequency |
|---|
5-15 | 14 |
|---|
15-25 | 9 |
|---|
25-35 | 11 |
|---|
35-45 | 6 |
|---|
Q.10. Calculate the range of the following dataset: 17,24,32,28,41,35,30.
Related Articles:
Similar Reads
Statistics in Maths Statistics is the science of collecting, organizing, analyzing, and interpreting information to uncover patterns, trends, and insights. Statistics allows us to see the bigger picture and tackle real-world problems like measuring the popularity of a new product, predicting the weather, or tracking he
3 min read
Statistics in Spreadsheets Microsoft office contains multiple applications that altogether serve as a complete information management system. A spreadsheet is among those tools and is very important when the analysis of data is required. A spreadsheet is defined as a large sheet that contains data and information arranged in
5 min read
Parameters and Statistics Statistics and parameters are two fundamental concepts in statistical theory. Although they may sound equal, there is a sharp difference between the two. One is used to represent the population, and the other is used to represent the sample. Now we will focus on the sample and population: Population
8 min read
Estimation in Statistics Estimation is a technique for calculating information about a bigger group from a smaller sample, and statistics are crucial to analyzing data. For instance, the average age of a city's population may be obtained by taking the age of a sample of 1,000 residents. While estimates aren't perfect, they
12 min read
Statistics Formulas Statistics is the branch of mathematics that involves collecting, analyzing, interpreting, presenting, and organizing data. It presents the data in an organized manner. It helps in making sense of large amounts of information by identifying patterns, trends, and relationships. Essentially, statistic
11 min read
Statistic vs Parameter In the statistical and data analytics areas, parameters and statistics are the most widely used two terms. Statistic is a numerical value calculated from a sample of data, whereas, Parameter is a numerical value that describes a characteristic of an entire population. This article will provide the m
7 min read