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<p>Last updated on<strong>September 25, 2025</strong></p>
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<p>Last updated on<strong>September 25, 2025</strong></p>
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<p>In statistics, the sample standard deviation is a measure of the amount of variation or dispersion of a set of values. It indicates how much the individual data points deviate from the sample mean. In this topic, we will learn the formula for calculating the sample standard deviation.</p>
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<p>In statistics, the sample standard deviation is a measure of the amount of variation or dispersion of a set of values. It indicates how much the individual data points deviate from the sample mean. In this topic, we will learn the formula for calculating the sample standard deviation.</p>
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<h2>List of Math Formula for Sample Standard Deviation</h2>
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<h2>List of Math Formula for Sample Standard Deviation</h2>
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<h2>Math Formula for Sample Standard Deviation</h2>
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<h2>Math Formula for Sample Standard Deviation</h2>
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<p>The sample<a>standard deviation</a>is the<a>square</a>root of the<a>variance</a>of the sample data. It is calculated using the formula: Sample standard deviation formula:</p>
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<p>The sample<a>standard deviation</a>is the<a>square</a>root of the<a>variance</a>of the sample data. It is calculated using the formula: Sample standard deviation formula:</p>
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<p>\( s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}\) where \(x_i \) are the data values, \(\bar{x}\) is the sample<a>mean</a>, and n is the<a>number</a>of data points.</p>
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<p>\( s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}\) where \(x_i \) are the data values, \(\bar{x}\) is the sample<a>mean</a>, and n is the<a>number</a>of data points.</p>
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<h2>Importance of Sample Standard Deviation Formula</h2>
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<h2>Importance of Sample Standard Deviation Formula</h2>
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<p>In<a>math</a>and real life, the sample standard deviation formula helps us analyze and understand data variability. Here are some important aspects of the sample standard deviation: </p>
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<p>In<a>math</a>and real life, the sample standard deviation formula helps us analyze and understand data variability. Here are some important aspects of the sample standard deviation: </p>
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<p>It provides insights into the spread and consistency of a dataset. </p>
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<p>It provides insights into the spread and consistency of a dataset. </p>
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<p>By understanding the sample standard deviation, students can better grasp concepts like data distribution,<a>probability</a>, and<a>inferential statistics</a>. </p>
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<p>By understanding the sample standard deviation, students can better grasp concepts like data distribution,<a>probability</a>, and<a>inferential statistics</a>. </p>
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<p>It helps in assessing the risk and reliability of data-driven decisions.</p>
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<p>It helps in assessing the risk and reliability of data-driven decisions.</p>
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<h2>Tips and Tricks to Memorize Sample Standard Deviation Formula</h2>
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<h2>Tips and Tricks to Memorize Sample Standard Deviation Formula</h2>
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<p>Students often find the sample standard deviation formula tricky and confusing. Here are some tips and tricks to master it: </p>
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<p>Students often find the sample standard deviation formula tricky and confusing. Here are some tips and tricks to master it: </p>
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<p>Break down the formula into parts: understand the calculation of mean, deviation, and variance before combining them. - Use real-life datasets for practice, such as analyzing daily temperatures or exam scores. </p>
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<p>Break down the formula into parts: understand the calculation of mean, deviation, and variance before combining them. - Use real-life datasets for practice, such as analyzing daily temperatures or exam scores. </p>
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<p>Create flashcards with each step of the formula for a quick recall, and make a formula chart for easy reference.</p>
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<p>Create flashcards with each step of the formula for a quick recall, and make a formula chart for easy reference.</p>
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<h2>Real-Life Applications of Sample Standard Deviation Formula</h2>
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<h2>Real-Life Applications of Sample Standard Deviation Formula</h2>
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<p>In real life, the sample standard deviation is crucial for understanding the variability in a data set. Here are some applications: </p>
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<p>In real life, the sample standard deviation is crucial for understanding the variability in a data set. Here are some applications: </p>
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<p>In finance, it measures the volatility of stock returns. </p>
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<p>In finance, it measures the volatility of stock returns. </p>
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<p>In quality control, it assesses the consistency of<a>product</a>manufacturing. </p>
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<p>In quality control, it assesses the consistency of<a>product</a>manufacturing. </p>
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<p>In research, it evaluates the variability in experimental data.</p>
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<p>In research, it evaluates the variability in experimental data.</p>
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<h2>Common Mistakes and How to Avoid Them While Using Sample Standard Deviation Formula</h2>
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<h2>Common Mistakes and How to Avoid Them While Using Sample Standard Deviation Formula</h2>
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<p>Students make errors when calculating the sample standard deviation. Here are some mistakes and ways to avoid them, to master the formula.</p>
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<p>Students make errors when calculating the sample standard deviation. Here are some mistakes and ways to avoid them, to master the formula.</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Find the sample standard deviation of the dataset: 2, 4, 4, 4, 5, 5, 7, 9?</p>
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<p>Find the sample standard deviation of the dataset: 2, 4, 4, 4, 5, 5, 7, 9?</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 sample standard deviation is approximately 2.14</p>
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<p>The sample standard deviation is approximately 2.14</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>First, calculate the mean: \(\bar{x} = \frac{2+4+4+4+5+5+7+9}{8} = 5\)</p>
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<p>First, calculate the mean: \(\bar{x} = \frac{2+4+4+4+5+5+7+9}{8} = 5\)</p>
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<p>Next, calculate the squared deviations and sum them: \((2-5)^2 + (4-5)^2 + (4-5)^2 + (4-5)^2 + (5-5)^2 + (5-5)^2 + (7-5)^2 + (9-5)^2 = 4 + 1 + 1 + 1 + 0 + 0 + 4 + 16 = 27\)</p>
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<p>Next, calculate the squared deviations and sum them: \((2-5)^2 + (4-5)^2 + (4-5)^2 + (4-5)^2 + (5-5)^2 + (5-5)^2 + (7-5)^2 + (9-5)^2 = 4 + 1 + 1 + 1 + 0 + 0 + 4 + 16 = 27\)</p>
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<p>Now, divide by n-1: \(\frac{27}{7} \approx 3.86\)</p>
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<p>Now, divide by n-1: \(\frac{27}{7} \approx 3.86\)</p>
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<p>Finally, take the square root: \(s \approx \sqrt{3.86} \approx 2.14\)</p>
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<p>Finally, take the square root: \(s \approx \sqrt{3.86} \approx 2.14\)</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>A sample dataset has values: 10, 12, 23, 23, 16, 23, 21, 16. Find the sample standard deviation.</p>
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<p>A sample dataset has values: 10, 12, 23, 23, 16, 23, 21, 16. Find the sample standard deviation.</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 sample standard deviation is approximately 5.19</p>
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<p>The sample standard deviation is approximately 5.19</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>First, calculate the mean: \(\bar{x} = \frac{10+12+23+23+16+23+21+16}{8} = 18\)</p>
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<p>First, calculate the mean: \(\bar{x} = \frac{10+12+23+23+16+23+21+16}{8} = 18\)</p>
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<p>Next, calculate the squared deviations and sum them: \((10-18)^2 + (12-18)^2 + (23-18)^2 + (23-18)^2 + (16-18)^2 + (23-18)^2 + (21-18)^2 + (16-18)^2 = 64 + 36 + 25 + 25 + 4 + 25 + 9 + 4 = 192\)</p>
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<p>Next, calculate the squared deviations and sum them: \((10-18)^2 + (12-18)^2 + (23-18)^2 + (23-18)^2 + (16-18)^2 + (23-18)^2 + (21-18)^2 + (16-18)^2 = 64 + 36 + 25 + 25 + 4 + 25 + 9 + 4 = 192\)</p>
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<p>Now, divide by n-1: \(\frac{192}{7} \approx 27.43\)</p>
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<p>Now, divide by n-1: \(\frac{192}{7} \approx 27.43\)</p>
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<p>Finally, take the square root: \(s \approx \sqrt{27.43} \approx 5.19\)</p>
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<p>Finally, take the square root: \(s \approx \sqrt{27.43} \approx 5.19\)</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQs on Sample Standard Deviation Formula</h2>
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<h2>FAQs on Sample Standard Deviation Formula</h2>
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<h3>1.What is the sample standard deviation formula?</h3>
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<h3>1.What is the sample standard deviation formula?</h3>
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<p>The formula to find the sample standard deviation is: \( s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}\) where \( x_i\) are the data values, \(\bar{x}\) is the sample mean, and n is the number of data points.</p>
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<p>The formula to find the sample standard deviation is: \( s = \sqrt{\frac{\sum (x_i - \bar{x})^2}{n-1}}\) where \( x_i\) are the data values, \(\bar{x}\) is the sample mean, and n is the number of data points.</p>
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<h3>2.How does sample standard deviation differ from population standard deviation?</h3>
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<h3>2.How does sample standard deviation differ from population standard deviation?</h3>
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<p>The sample standard deviation uses n-1 in the<a>denominator</a>to account for bias when estimating the population standard deviation, while the population standard deviation uses n .</p>
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<p>The sample standard deviation uses n-1 in the<a>denominator</a>to account for bias when estimating the population standard deviation, while the population standard deviation uses n .</p>
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<h3>3.Why is the sample standard deviation important?</h3>
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<h3>3.Why is the sample standard deviation important?</h3>
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<p>The sample standard deviation is crucial for understanding data variability, assessing risk, and making data-driven decisions.</p>
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<p>The sample standard deviation is crucial for understanding data variability, assessing risk, and making data-driven decisions.</p>
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<h3>4.What does a high sample standard deviation indicate?</h3>
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<h3>4.What does a high sample standard deviation indicate?</h3>
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<p>A high sample standard deviation indicates that the data points are spread out over a wide range of values, showing more variability.</p>
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<p>A high sample standard deviation indicates that the data points are spread out over a wide range of values, showing more variability.</p>
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<h3>5.Can sample standard deviation be negative?</h3>
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<h3>5.Can sample standard deviation be negative?</h3>
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<p>No, the sample standard deviation cannot be negative because it is derived from squared values and represents a measure of spread.</p>
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<p>No, the sample standard deviation cannot be negative because it is derived from squared values and represents a measure of spread.</p>
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<h2>Glossary for Sample Standard Deviation</h2>
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<h2>Glossary for Sample Standard Deviation</h2>
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<ul><li><strong>Sample Standard Deviation:</strong>A measure of the amount of variation or dispersion in a set of sample data values.</li>
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<ul><li><strong>Sample Standard Deviation:</strong>A measure of the amount of variation or dispersion in a set of sample data values.</li>
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</ul><ul><li><strong>Variance:</strong>The<a>average</a>of the squared differences from the mean.</li>
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</ul><ul><li><strong>Variance:</strong>The<a>average</a>of the squared differences from the mean.</li>
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</ul><ul><li><strong>Mean (Sample Mean):</strong>The<a>sum</a>of all the data values divided by the number of data points in the sample.</li>
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</ul><ul><li><strong>Mean (Sample Mean):</strong>The<a>sum</a>of all the data values divided by the number of data points in the sample.</li>
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</ul><ul><li><strong>Squared Deviation:</strong>The square of the difference between a data value and the mean.</li>
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</ul><ul><li><strong>Squared Deviation:</strong>The square of the difference between a data value and the mean.</li>
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</ul><ul><li><strong>Bias Correction:</strong>The adjustment made by using n-1 in the sample standard deviation formula to estimate the population standard deviation accurately.</li>
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</ul><ul><li><strong>Bias Correction:</strong>The adjustment made by using n-1 in the sample standard deviation formula to estimate the population standard deviation accurately.</li>
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</ul><h2>Jaskaran Singh Saluja</h2>
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</ul><h2>Jaskaran Singh Saluja</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>