Statistics

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?

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

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

Univariate frequency distribution (A) 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?

aσ / c (D) 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?

Correlation (C) Signup and view all the answers

Which type of distribution involves two discrete variables?

Bivariate distribution (A) 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?

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

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

Univariate distribution (B) 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?

8 (B) 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?

r (D) 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?

9/4 (D) Signup and view all the answers

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

10 (A) 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?

4 (D) Signup and view all the answers

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

∑f|x - M| / n (C) Signup and view all the answers

What is the coefficient of standard deviation?

The ratio of the standard deviation to the mean (A) Signup and view all the answers

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

Mean deviation / Median (C) Signup and view all the answers

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

S^2 = σ^2 + d^2 (A) Signup and view all the answers

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

√(∑(x - x)² / N) (A) Signup and view all the answers

What is the variance of a distribution?

The square of the standard deviation (D) Signup and view all the answers

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

σ (C) Signup and view all the answers

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

Mean deviation from the median (C) Signup and view all the answers

What is the mean square deviation?

The average of the squared deviations from an arbitrary number (D) Signup and view all the answers

What is the coefficient of variation?

The ratio of the standard deviation to the mean (C) Signup and view all the answers

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 (D) 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?

68.27% for X ± σ, 95.45% for X ± 2σ, and 99.74% for X ± 3σ (B) Signup and view all the answers

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

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

What is the relation between mean deviation and standard deviation?

Mean deviation ≈ (standard deviation) / √2 (C) Signup and view all the answers

What is the measure of skewness denoted by γ₁?

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