Gr 11 Math Ch 11: Varience and Standard Deviation
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Questions and Answers

What is the formula for variance?

  • $\sigma^2 = (x_i - \bar{x})^2$
  • $\sigma^2 = \frac{\sum_{i=1}^{n} x_i}{n}$
  • $\sigma^2 = \sum_{i=1}^{n} (x_i - \bar{x})$
  • $\sigma^2 = \frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n}$ (correct)

    • What is the main purpose of calculating variance?

  • To measure the spread of data around the mean (correct)
  • To find the median of the data
  • To find the mean of the data
  • To identify outliers in the data

    • What is the unit of standard deviation?

  • Squared units
  • Different units
  • The same units as the original data (correct)
  • No units

    • What does a small standard deviation indicate?

    <p>Low variability in the data</p> Signup and view all the answers

    What is the formula for standard deviation?

    <p>$\sigma = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \bar{x})^2}{n}}$</p> Signup and view all the answers

    What is the sixth step in calculating variance and standard deviation?

    <p>Take the square root of the variance to find the standard deviation</p> Signup and view all the answers

    What does a large standard deviation indicate?

    <p>High variability in the data</p> Signup and view all the answers

    Why is variance always non-negative?

    <p>Because each term in the variance sum is squared</p> Signup and view all the answers

    What is the main purpose of calculating the variance of a data set?

    <p>To measure the spread of data around the mean</p> Signup and view all the answers

    Which of the following statements about the variance is true?

    <p>Variance is always non-negative</p> Signup and view all the answers

    What is the relationship between the standard deviation and the variance of a data set?

    <p>The standard deviation is the square root of the variance</p> Signup and view all the answers

    What is the purpose of calculating the standard deviation of a data set?

    <p>To measure the spread of data around the mean</p> Signup and view all the answers

    Which of the following statements about the standard deviation is true?

    <p>The standard deviation has the same units as the original data</p> Signup and view all the answers

    What is the correct sequence of steps to calculate the variance and standard deviation of a data set?

    <p>Calculate the mean, then calculate each deviation, then square each deviation, then sum the squared deviations, then divide by the number of data points</p> Signup and view all the answers

    What does a large standard deviation indicate about the data?

    <p>The data values are spread out over a larger range</p> Signup and view all the answers

    What is the main difference between the variance and the standard deviation?

    <p>The variance has squared units, while the standard deviation has the same units as the original data</p> Signup and view all the answers

    Which of the following is a reason why the variance of a data set is not directly comparable with the mean or the data themselves?

    <p>Because variance has squared units</p> Signup and view all the answers

    What does a small standard deviation indicate about the data points?

    <p>They are close to the mean, indicating low variability</p> Signup and view all the answers

    What is the purpose of calculating the variance of a data set?

    <p>To measure the spread of the data around the mean</p> Signup and view all the answers

    Which of the following is a property of standard deviation?

    <p>It is always a positive number</p> Signup and view all the answers

    What is the result of dividing the sum of the squared deviations by the number of data points?

    <p>The variance</p> Signup and view all the answers

    What is the purpose of calculating the squared deviations?

    <p>To find the variance of the data set</p> Signup and view all the answers

    Which of the following is a step in calculating the variance and standard deviation?

    <p>Calculate each deviation from the mean</p> Signup and view all the answers

    What is the relationship between the standard deviation and the variance of a data set?

    <p>The standard deviation is the square root of the variance</p> Signup and view all the answers

    What is the main difference between the variance and standard deviation of a data set?

    <p>Variance has squared units, while standard deviation has the same units as the data.</p> Signup and view all the answers

    What is the effect of squaring each deviation from the mean on the variance?

    <p>It makes the variance more sensitive to outliers.</p> Signup and view all the answers

    What is the implication of having a large standard deviation on the interpretation of the data?

    <p>The data points are spread out over a large range of values.</p> Signup and view all the answers

    What is the purpose of calculating the variance of a data set?

    <p>To measure the spread of the data around the mean.</p> Signup and view all the answers

    What happens to the variance when the data points are multiplied by a constant?

    <p>The variance is multiplied by the square of the constant.</p> Signup and view all the answers

    What is the relationship between the variance and standard deviation of a data set?

    <p>The standard deviation is the square root of the variance.</p> Signup and view all the answers

    What is the effect of having a small standard deviation on the interpretation of the data?

    <p>The data points are closely clustered around the mean.</p> Signup and view all the answers

    Why is the variance of a data set always non-negative?

    <p>Because each term in the variance sum is squared.</p> Signup and view all the answers

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