Statistics
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Questions and Answers

What is the term for the function that assigns frequencies to pairs (xi, yj)?

  • Univariate frequency distribution
  • Correlation coefficient
  • Bivariate frequency distribution (correct)
  • Joint probability distribution

    • What is the purpose of calculating the covariance between two variables?

  • To determine the mean of the variables
  • To measure the strength and direction of the linear relationship (correct)
  • To determine the correlation coefficient
  • To find the standard deviation of the variables

    • What happens to the covariance when the origin of the variables is changed?

  • It increases
  • It decreases
  • It remains unchanged (correct)
  • It changes sign

    • What is the formula for calculating the covariance between two variables?

    <p>$\frac{1}{n} \sum(x_i - \bar{x})(y_i - \bar{y})$</p> Signup and view all the answers

    What is the term for the distribution of the values of a single variable?

    <p>Univariate frequency distribution</p> Signup and view all the answers

    What is the new standard deviation of the variate y = ax + b / c, in terms of the standard deviation σ of the variate x?

    <p>aσ / c</p> Signup and view all the answers

    What is the term used to describe the relationship between two variables that always fluctuate in the same or opposite directions?

    <p>Correlation</p> Signup and view all the answers

    Which type of distribution involves two discrete variables?

    <p>Bivariate distribution</p> Signup and view all the answers

    What is the formula to calculate the new variance of the variate y = ax + b / c, in terms of the variance of the variate x?

    <p>(a / c)^2 * variance of x</p> Signup and view all the answers

    What is the term used to describe a distribution involving only one variable?

    <p>Univariate distribution</p> Signup and view all the answers

    If the variance of x is 4, and the covariance of x and y is 16, what is the variance of y?

    <p>8</p> Signup and view all the answers

    What is the correlation coefficient between AX + B and CY + D, if the correlation coefficient between x and y is r?

    <p>r</p> Signup and view all the answers

    If the covariance of x and y is 5, and the variance of x is 4, what is the variance of y?

    <p>9/4</p> Signup and view all the answers

    If ∑x = 50, ∑y = 60, and ∑xy = 350, what is the covariance of x and y?

    <p>10</p> Signup and view all the answers

    If the standard deviation of x is 2, and the covariance of x and y is 8, what is the standard deviation of y?

    <p>4</p> Signup and view all the answers

    What is the formula to calculate the mean deviation from a continuous series?

    <p>∑f|x - M| / n</p> Signup and view all the answers

    What is the coefficient of standard deviation?

    <p>The ratio of the standard deviation to the mean</p> Signup and view all the answers

    What is the coefficient of dispersion based on the mean deviation from the median?

    <p>Mean deviation / Median</p> Signup and view all the answers

    What is the relationship between the standard deviation and the root mean square deviation?

    <p>S^2 = σ^2 + d^2</p> Signup and view all the answers

    What is the formula to calculate the standard deviation from an individual series?

    <p>√(∑(x - x)² / N)</p> Signup and view all the answers

    What is the variance of a distribution?

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

    What is the symbol commonly used to represent the standard deviation?

    <p>σ</p> Signup and view all the answers

    What does the term 'mean deviation' typically refer to?

    <p>Mean deviation from the median</p> Signup and view all the answers

    What is the mean square deviation?

    <p>The average of the squared deviations from an arbitrary number</p> Signup and view all the answers

    What is the coefficient of variation?

    <p>The ratio of the standard deviation to the mean</p> Signup and view all the answers

    What is the relationship between the range and standard deviation of a series?

    <p>Range is widely used in statistical series relating to quality control in production and standard deviation ≤ Range</p> Signup and view all the answers

    What percentage of items are covered in a symmetrical distribution if the mean is X and the standard deviation is σ?

    <p>68.27% for X ± σ, 95.45% for X ± 2σ, and 99.74% for X ± 3σ</p> Signup and view all the answers

    What is the formula to calculate the variance of the combined series?

    <p>σ² = (n₁(x₁ - x)² + n₂(x₂ - x)²) / (n₁ + n₂)</p> Signup and view all the answers

    What is the relation between mean deviation and standard deviation?

    <p>Mean deviation ≈ (standard deviation) / √2</p> Signup and view all the answers

    What is the measure of skewness denoted by γ₁?

    <p>γ₁ = ∑(xi - μ)³ / (∑(xi - μ)²)³/²</p> Signup and view all the answers

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