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<p>Last updated on<strong>November 27, 2025</strong></p>
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<p>Last updated on<strong>November 27, 2025</strong></p>
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<p>The range is the difference between the highest and lowest values of a given data set. The range helps us in understanding the spread of a data. Range is a measure of dispersion. In this topic, we will learn more about range, its formulas, how to calculate, and so on.</p>
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<p>The range is the difference between the highest and lowest values of a given data set. The range helps us in understanding the spread of a data. Range is a measure of dispersion. In this topic, we will learn more about range, its formulas, how to calculate, and so on.</p>
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<h2>What is Range?</h2>
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<h2>What is Range?</h2>
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<p>In<a>statistics</a>, the range is used to describe the<a>spread of data</a>in a dataset. The range in<a>math</a>is the difference between the smallest and largest values. This simple calculation shows how much the values differ and gives a basic idea of the data’s overall spread.</p>
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<p>In<a>statistics</a>, the range is used to describe the<a>spread of data</a>in a dataset. The range in<a>math</a>is the difference between the smallest and largest values. This simple calculation shows how much the values differ and gives a basic idea of the data’s overall spread.</p>
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<p>However, the definition of range in math also comes with limitations. The range only considers the lower and upper values and does not account for how the other<a>data</a>points are distributed. It also ignores the<a></a><a>number</a>of data points in the dataset. Because of this, the range can be misleading when there are<a>outliers</a>, since excessively high or low values can significantly affect the result.</p>
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<p>However, the definition of range in math also comes with limitations. The range only considers the lower and upper values and does not account for how the other<a>data</a>points are distributed. It also ignores the<a></a><a>number</a>of data points in the dataset. Because of this, the range can be misleading when there are<a>outliers</a>, since excessively high or low values can significantly affect the result.</p>
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<p>For example,</p>
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<p>For example,</p>
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<p>Consider the dataset as,</p>
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<p>Consider the dataset as,</p>
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<p>12, 18, 25, 30, 37</p>
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<p>12, 18, 25, 30, 37</p>
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<p>Highest value = 37</p>
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<p>Highest value = 37</p>
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<p>Lowest value = 12</p>
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<p>Lowest value = 12</p>
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<p>Now,</p>
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<p>Now,</p>
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<p>The range = \(37-12 = 25\)</p>
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<p>The range = \(37-12 = 25\)</p>
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<h2>How to Calculate Range in Statistics?</h2>
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<h2>How to Calculate Range in Statistics?</h2>
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<p>As discussed, range is the difference between the upper and lower values. So, the<a>formula</a>to calculate the range is \( R = H - L\), where R is the range, H is the maximum value, and L is the minimum value.</p>
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<p>As discussed, range is the difference between the upper and lower values. So, the<a>formula</a>to calculate the range is \( R = H - L\), where R is the range, H is the maximum value, and L is the minimum value.</p>
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<p>Follow these steps to calculate the range - \(\text{Range} = \text{Maximum value} - \text{Minimum value} \)</p>
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<p>Follow these steps to calculate the range - \(\text{Range} = \text{Maximum value} - \text{Minimum value} \)</p>
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<p><strong>Step 1:</strong>Arrange the<a>data</a><a>set</a>in<a>ascending order</a></p>
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<p><strong>Step 1:</strong>Arrange the<a>data</a><a>set</a>in<a>ascending order</a></p>
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<p><strong>Step 2:</strong>Identify the upper and lower limits from the dataset</p>
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<p><strong>Step 2:</strong>Identify the upper and lower limits from the dataset</p>
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<p><strong>Step 3:</strong>Finding the range using the formula; \(\text{Range} = \text{Maximum value} - \text{Minimum value} \).</p>
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<p><strong>Step 3:</strong>Finding the range using the formula; \(\text{Range} = \text{Maximum value} - \text{Minimum value} \).</p>
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<p>For instance, find the range<a>of</a>the given dataset: \(5, 12, 8, 20, 15\) </p>
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<p>For instance, find the range<a>of</a>the given dataset: \(5, 12, 8, 20, 15\) </p>
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<p><strong>Step 1:</strong>Arrange the data set in order</p>
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<p><strong>Step 1:</strong>Arrange the data set in order</p>
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<p>That is \(5, 8, 12, 15, 20\)</p>
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<p>That is \(5, 8, 12, 15, 20\)</p>
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<p><strong>Step 2:</strong>Identify the upper and lower limits from the dataset</p>
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<p><strong>Step 2:</strong>Identify the upper and lower limits from the dataset</p>
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<p>The upper limit is 20</p>
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<p>The upper limit is 20</p>
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<p>The lower limit is 5</p>
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<p>The lower limit is 5</p>
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<p><strong>Step 3:</strong>Find the difference between the minimum and maximum value.</p>
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<p><strong>Step 3:</strong>Find the difference between the minimum and maximum value.</p>
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<p>Range = \(20 - 5 = 15\)</p>
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<p>Range = \(20 - 5 = 15\)</p>
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<h2>What is the Rule of Thumb?</h2>
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<h2>What is the Rule of Thumb?</h2>
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<p>According to the rule of thumb, most of the data values fall within four standard deviations, that is, two standard deviations above the<a>mean</a>and two standard deviations below the mean. The formula for<a>standard deviation</a>(σ) is,</p>
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<p>According to the rule of thumb, most of the data values fall within four standard deviations, that is, two standard deviations above the<a>mean</a>and two standard deviations below the mean. The formula for<a>standard deviation</a>(σ) is,</p>
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<p>\(\sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}} \)</p>
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<p>\(\sigma = \sqrt{\frac{\sum (x_i - \mu)^2}{N}} \)</p>
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<h2>What are the Limitations of Range?</h2>
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<h2>What are the Limitations of Range?</h2>
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<p>The range is easy to calculate, but it has several drawbacks: </p>
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<p>The range is easy to calculate, but it has several drawbacks: </p>
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<ul><li>It does not provide information about how many data points are in the dataset. </li>
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<ul><li>It does not provide information about how many data points are in the dataset. </li>
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<li>It cannot be used to determine other measures, like the mean,<a>median</a>, or<a>mode</a>. </li>
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<li>It cannot be used to determine other measures, like the mean,<a>median</a>, or<a>mode</a>. </li>
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<li>It is highly sensitive to outliers, meaning extreme values can significantly change the range. </li>
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<li>It is highly sensitive to outliers, meaning extreme values can significantly change the range. </li>
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<li>It is not suitable for open-ended distributions.</li>
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<li>It is not suitable for open-ended distributions.</li>
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</ul><h2>Range Formula</h2>
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</ul><h2>Range Formula</h2>
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<p>The formula used to calculate the range of a dataset is,</p>
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<p>The formula used to calculate the range of a dataset is,</p>
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<p>\(\text{Range} = \text{Maximum value} - \text{Minimum value} \)</p>
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<p>\(\text{Range} = \text{Maximum value} - \text{Minimum value} \)</p>
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<p>In<a>addition</a>to this basic formula, there are specific methods for finding the range of both grouped and ungrouped data.</p>
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<p>In<a>addition</a>to this basic formula, there are specific methods for finding the range of both grouped and ungrouped data.</p>
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<h2>Range of Ungrouped Data</h2>
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<h2>Range of Ungrouped Data</h2>
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<p>For continuous frequency distributions or grouped data, the range is calculated as the difference between the upper boundary of the highest<a>class interval</a>and the lower boundary of the lowest class interval. It is one of the simplest<a>measures of dispersion</a>and provides an overall idea of how spread out the observations are.</p>
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<p>For continuous frequency distributions or grouped data, the range is calculated as the difference between the upper boundary of the highest<a>class interval</a>and the lower boundary of the lowest class interval. It is one of the simplest<a>measures of dispersion</a>and provides an overall idea of how spread out the observations are.</p>
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<p>The formula to calculate the range for grouped data is:</p>
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<p>The formula to calculate the range for grouped data is:</p>
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<p>Range = Upper class boundary of the highest interval - Lower class boundary of the lowest interval.</p>
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<p>Range = Upper class boundary of the highest interval - Lower class boundary of the lowest interval.</p>
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<h2>Range of Grouped Data</h2>
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<h2>Range of Grouped Data</h2>
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<p>For continuous<a>frequency distribution</a>or grouped data, the range is the difference between the upper boundary of the highest class interval and the lower boundary of the lowest class interval. It is one of the simplest measures of dispersion and provides a clear picture of the data's overall spread.</p>
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<p>For continuous<a>frequency distribution</a>or grouped data, the range is the difference between the upper boundary of the highest class interval and the lower boundary of the lowest class interval. It is one of the simplest measures of dispersion and provides a clear picture of the data's overall spread.</p>
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<p>The formula for calculating the range of grouped data is,</p>
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<p>The formula for calculating the range of grouped data is,</p>
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<p>Range = Upper class boundary of the highest interval - Lower class boundary of the lowest interval.</p>
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<p>Range = Upper class boundary of the highest interval - Lower class boundary of the lowest interval.</p>
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<h2>Tips and Tricks to Master Range of Statistics</h2>
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<h2>Tips and Tricks to Master Range of Statistics</h2>
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<p>The range of statistics is a complex mathematical topic; however, with some tips and tricks, it can be better understood. Some valuable tips and tricks are mentioned below. </p>
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<p>The range of statistics is a complex mathematical topic; however, with some tips and tricks, it can be better understood. Some valuable tips and tricks are mentioned below. </p>
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<ul><li>Make sure to carefully review your dataset to identify the actual highest and lowest values before calculating the range. </li>
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<ul><li>Make sure to carefully review your dataset to identify the actual highest and lowest values before calculating the range. </li>
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</ul><ul><li>Put your numbers from smallest to largest or largest to smallest; it helps you easily find the smallest and largest values. </li>
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</ul><ul><li>Put your numbers from smallest to largest or largest to smallest; it helps you easily find the smallest and largest values. </li>
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</ul><ul><li>Big or small<a>odd numbers</a>can change the range, so make sure to check for any unusual values in your data. </li>
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</ul><ul><li>Big or small<a>odd numbers</a>can change the range, so make sure to check for any unusual values in your data. </li>
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</ul><ul><li>When<a>comparing</a>two sets of data, a larger range indicates the values vary widely, while a smaller range suggests the data is steadier and consistent. </li>
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</ul><ul><li>When<a>comparing</a>two sets of data, a larger range indicates the values vary widely, while a smaller range suggests the data is steadier and consistent. </li>
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</ul><ul><li>Try using the range with real-life examples such as temperature changes, exam marks, or stock prices. It helps you better understand the concept and see how it works in everyday situations.</li>
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</ul><ul><li>Try using the range with real-life examples such as temperature changes, exam marks, or stock prices. It helps you better understand the concept and see how it works in everyday situations.</li>
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<li>Parents can use familiar situations, such as children’s heights in class, daily temperatures, or pocket<a>money</a>, to explain how a range shows the spread of values.</li>
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<li>Parents can use familiar situations, such as children’s heights in class, daily temperatures, or pocket<a>money</a>, to explain how a range shows the spread of values.</li>
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<li>Teachers and parents can show children how to calculate the range for grouped data using class intervals.</li>
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<li>Teachers and parents can show children how to calculate the range for grouped data using class intervals.</li>
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<li>Children can better understand the concept when it relates to their everyday life.</li>
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<li>Children can better understand the concept when it relates to their everyday life.</li>
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</ul><h2>Common Mistakes and How to Avoid Them in Range of Statistics</h2>
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</ul><h2>Common Mistakes and How to Avoid Them in Range of Statistics</h2>
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<p>Range is used to find the spread of the data. When finding the range in statistics students tend to make mistakes, let’s learn some common mistakes and ways to avoid them. </p>
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<p>Range is used to find the spread of the data. When finding the range in statistics students tend to make mistakes, let’s learn some common mistakes and ways to avoid them. </p>
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<h2>Real-World Applications of Range in Statistics</h2>
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<h2>Real-World Applications of Range in Statistics</h2>
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<p>The concept of range has numerous applications across various fields. Now let’s learn a few applications of range in statistics. </p>
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<p>The concept of range has numerous applications across various fields. Now let’s learn a few applications of range in statistics. </p>
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<ul><li>We use range to compare the prices of similar products; we use range to understand the price spread and to get an understanding of the budget. </li>
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<ul><li>We use range to compare the prices of similar products; we use range to understand the price spread and to get an understanding of the budget. </li>
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<li> To analyze the performance of the students in an exam, we use range. </li>
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<li> To analyze the performance of the students in an exam, we use range. </li>
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<li>To analyze the performance of the players in sports, range is used.</li>
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<li>To analyze the performance of the players in sports, range is used.</li>
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<li>Meteorologists use the range to show the difference between the highest and lowest temperatures in a day, week, or month to analyze climate patterns.</li>
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<li>Meteorologists use the range to show the difference between the highest and lowest temperatures in a day, week, or month to analyze climate patterns.</li>
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<li>Teachers use the range of students’ marks to measure the variation in performance within a class or across<a>multiple</a>tests.</li>
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<li>Teachers use the range of students’ marks to measure the variation in performance within a class or across<a>multiple</a>tests.</li>
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</ul><h3>Problem 1</h3>
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</ul><h3>Problem 1</h3>
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<p>A teacher recorded the ages of five students in a classroom: 12, 14, 15, 13, and 16 years old. Find the range of their ages.</p>
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<p>A teacher recorded the ages of five students in a classroom: 12, 14, 15, 13, and 16 years old. Find the range of their ages.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The range of their ages is 4 years. </p>
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<p>The range of their ages is 4 years. </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The given data in ascending order is 12, 13, 14, 15, 16</p>
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<p>The given data in ascending order is 12, 13, 14, 15, 16</p>
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<p>The upper limit is 16</p>
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<p>The upper limit is 16</p>
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<p>The lower limit is 12</p>
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<p>The lower limit is 12</p>
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<p>The range = \(16 - 12 = 4\)</p>
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<p>The range = \(16 - 12 = 4\)</p>
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<p>The range of their age is 4. </p>
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<p>The range of their age is 4. </p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<h3>Problem 2</h3>
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<p>The heights (in inches) of five basketball players are: 68, 72, 75, 70, and 78 inches. Find the range of their heights.</p>
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<p>The heights (in inches) of five basketball players are: 68, 72, 75, 70, and 78 inches. Find the range of their heights.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p> The range of their heights is 10 inches.</p>
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<p> The range of their heights is 10 inches.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The given dataset in ascending order is 68, 70, 72, 75, 78</p>
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<p>The given dataset in ascending order is 68, 70, 72, 75, 78</p>
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<p>The upper limit is 78</p>
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<p>The upper limit is 78</p>
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<p>The lower limit is 68</p>
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<p>The lower limit is 68</p>
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<p>The range of heights = \( 78 - 68 = 10\) inches. </p>
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<p>The range of heights = \( 78 - 68 = 10\) inches. </p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<h3>Problem 3</h3>
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<p>A shopkeeper recorded the number of customers visiting his shop over five days: 45, 38, 50, 42, and 47. Determine the range of customers.</p>
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<p>A shopkeeper recorded the number of customers visiting his shop over five days: 45, 38, 50, 42, and 47. Determine the range of customers.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The range of customers is 12.</p>
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<p>The range of customers is 12.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>The given dataset in ascending order is 38, 42, 45, 47, 50</p>
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<p>The given dataset in ascending order is 38, 42, 45, 47, 50</p>
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<p>The upper limit is 50</p>
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<p>The upper limit is 50</p>
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<p>The lower limit is 38</p>
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<p>The lower limit is 38</p>
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<p>The range of customers = \(50 - 38 = 12\). </p>
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<p>The range of customers = \(50 - 38 = 12\). </p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<h3>Problem 4</h3>
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<p>The temperatures (in °C) recorded in a city over five days are: 32, 29, 35, 31, and 30. Find the range of temperatures.</p>
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<p>The temperatures (in °C) recorded in a city over five days are: 32, 29, 35, 31, and 30. Find the range of temperatures.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The range of the temperatures is 6 °C. </p>
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<p>The range of the temperatures is 6 °C. </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p> The given dataset in ascending order is 29, 30, 31, 32, 35, </p>
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<p> The given dataset in ascending order is 29, 30, 31, 32, 35, </p>
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<p>The upper limit is 35</p>
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<p>The upper limit is 35</p>
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<p>The lower limit is 29</p>
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<p>The lower limit is 29</p>
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<p>The range of temperatures = \( 35 - 29 = 6 °C.\) </p>
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<p>The range of temperatures = \( 35 - 29 = 6 °C.\) </p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 5</h3>
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<h3>Problem 5</h3>
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<p>A student recorded the number of pages read each day for a week: 20, 15, 18, 22, 25, 30, and 27. Find the range of pages read.</p>
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<p>A student recorded the number of pages read each day for a week: 20, 15, 18, 22, 25, 30, and 27. Find the range of pages read.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The range of pages read is 15 pages.</p>
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<p>The range of pages read is 15 pages.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p> The given dataset in ascending order is 15, 18, 20, 22, 25, 27, 30</p>
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<p> The given dataset in ascending order is 15, 18, 20, 22, 25, 27, 30</p>
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<p>The upper limit is 30</p>
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<p>The upper limit is 30</p>
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<p>The lower limit is 15</p>
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<p>The lower limit is 15</p>
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<p>The range of pages read = \(30 - 15 = 15.\)</p>
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<p>The range of pages read = \(30 - 15 = 15.\)</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQs on Range in Statistics</h2>
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<h2>FAQs on Range in Statistics</h2>
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<h3>1.What is the range in statistics?</h3>
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<h3>1.What is the range in statistics?</h3>
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<p>The range is the measure of dispersion, it is the difference between the upper and lower limit of the dataset. </p>
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<p>The range is the measure of dispersion, it is the difference between the upper and lower limit of the dataset. </p>
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<h3>2.How is the range calculated?</h3>
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<h3>2.How is the range calculated?</h3>
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<p>The range is calculated by subtracting the upper limit from the lower limit. </p>
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<p>The range is calculated by subtracting the upper limit from the lower limit. </p>
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<h3>3. What is the use of range?</h3>
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<h3>3. What is the use of range?</h3>
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<p>Range is used to analyze how the data is spread in a dataset. </p>
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<p>Range is used to analyze how the data is spread in a dataset. </p>
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<h3>4.Can the range be negative?</h3>
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<h3>4.Can the range be negative?</h3>
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<p>No, the range cannot be negative. Because the range is calculated by subtracting the upper limit from the lower limit. </p>
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<p>No, the range cannot be negative. Because the range is calculated by subtracting the upper limit from the lower limit. </p>
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<h3>5.What does a high range indicate?</h3>
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<h3>5.What does a high range indicate?</h3>
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<p>The high range indicates that there is a large spread between the smallest and largest values. </p>
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<p>The high range indicates that there is a large spread between the smallest and largest values. </p>
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<h2>Jaipreet Kour Wazir</h2>
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<h2>Jaipreet Kour Wazir</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<p>Jaipreet Kour Wazir is a data wizard with over 5 years of expertise in simplifying complex data concepts. From crunching numbers to crafting insightful visualizations, she turns raw data into compelling stories. Her journey from analytics to education ref</p>
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<p>Jaipreet Kour Wazir is a data wizard with over 5 years of expertise in simplifying complex data concepts. From crunching numbers to crafting insightful visualizations, she turns raw data into compelling stories. Her journey from analytics to education ref</p>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: She compares datasets to puzzle games-the more you play with them, the clearer the picture becomes!</p>
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<p>: She compares datasets to puzzle games-the more you play with them, the clearer the picture becomes!</p>