30 Questions
What is the term for the function that assigns frequencies to pairs (xi, yj)?
Bivariate frequency distribution
What is the purpose of calculating the covariance between two variables?
To measure the strength and direction of the linear relationship
What happens to the covariance when the origin of the variables is changed?
It remains unchanged
What is the formula for calculating the covariance between two variables?
$\frac{1}{n} \sum(x_i - \bar{x})(y_i - \bar{y})$
What is the term for the distribution of the values of a single variable?
Univariate frequency distribution
What is the new standard deviation of the variate y = ax + b / c, in terms of the standard deviation σ of the variate x?
aσ / c
What is the term used to describe the relationship between two variables that always fluctuate in the same or opposite directions?
Correlation
Which type of distribution involves two discrete variables?
Bivariate distribution
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?
(a / c)^2 * variance of x
What is the term used to describe a distribution involving only one variable?
Univariate distribution
If the variance of x is 4, and the covariance of x and y is 16, what is the variance of y?
8
What is the correlation coefficient between AX + B and CY + D, if the correlation coefficient between x and y is r?
r
If the covariance of x and y is 5, and the variance of x is 4, what is the variance of y?
9/4
If ∑x = 50, ∑y = 60, and ∑xy = 350, what is the covariance of x and y?
10
If the standard deviation of x is 2, and the covariance of x and y is 8, what is the standard deviation of y?
4
What is the formula to calculate the mean deviation from a continuous series?
∑f|x - M| / n
What is the coefficient of standard deviation?
The ratio of the standard deviation to the mean
What is the coefficient of dispersion based on the mean deviation from the median?
Mean deviation / Median
What is the relationship between the standard deviation and the root mean square deviation?
S^2 = σ^2 + d^2
What is the formula to calculate the standard deviation from an individual series?
√(∑(x - x)² / N)
What is the variance of a distribution?
The square of the standard deviation
What is the symbol commonly used to represent the standard deviation?
σ
What does the term 'mean deviation' typically refer to?
Mean deviation from the median
What is the mean square deviation?
The average of the squared deviations from an arbitrary number
What is the coefficient of variation?
The ratio of the standard deviation to the mean
What is the relationship between the range and standard deviation of a series?
Range is widely used in statistical series relating to quality control in production and standard deviation ≤ Range
What percentage of items are covered in a symmetrical distribution if the mean is X and the standard deviation is σ?
68.27% for X ± σ, 95.45% for X ± 2σ, and 99.74% for X ± 3σ
What is the formula to calculate the variance of the combined series?
σ² = (n₁(x₁ - x)² + n₂(x₂ - x)²) / (n₁ + n₂)
What is the relation between mean deviation and standard deviation?
Mean deviation ≈ (standard deviation) / √2
What is the measure of skewness denoted by γ₁?
γ₁ = ∑(xi - μ)³ / (∑(xi - μ)²)³/²
Test your knowledge of measures of central tendency with this quiz. Calculate standard deviations and more with these practice questions. Study guide for statistics students.
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