Transformation

Front

What is a transformation in statistics?

Back

A transformation in statistics refers to a mathematical operation applied to a random variable to change its scale or distribution, such as converting units (e.g., feet to inches).

Front

How do you calculate the mean of a transformed variable?

Back

To calculate the mean of a transformed variable, apply the transformation to the original mean. For example, if the original mean is \(\mu\) and the transformation is multiplying by a constant \(c\), the new mean is \(c \cdot \mu\).

Front

What is the formula for the standard deviation of a transformed variable?

Back

The standard deviation of a transformed variable is calculated by multiplying the original standard deviation by the absolute value of the transformation factor. If the transformation is \(Y = cX\), then \(\sigma_Y = |c| \cdot \sigma_X\).

Front

What is variance, and how is it calculated?

Back

Variance is a measure of the dispersion of a set of values. It is calculated as the average of the squared differences from the mean: \(\sigma^2 = \frac{1}{N} \sum_{i=1}^{N} (x_i - \mu)^2\).

Front

How do you find the standard deviation from variance?

Back

The standard deviation is the square root of the variance: \(\sigma = \sqrt{\sigma^2}\).

Front

What is the mean weight of Will's lunch if he brings two ham sandwiches and three bananas?

Back

The mean weight is calculated as: \(2 \cdot 6 + 3 \cdot 8 = 12 + 24 = 36\) ounces.

Front

What is the relationship between mean and standard deviation in a transformation?

Back

In a transformation, the mean changes according to the transformation applied, while the standard deviation changes based on the scaling factor of the transformation.

Front

What is the difference between a transformation and a combination in statistics?

Back

A transformation changes the scale or units of a variable, while a combination involves adding or averaging multiple variables together.

Front

How do you convert feet to inches in terms of mean and standard deviation?

Back

To convert feet to inches, multiply the mean in feet by 12 and the standard deviation in feet by 12.

Front

What is the formula for the mean of a sum of random variables?

Back

The mean of a sum of random variables is the sum of their means: \(\mu_{X+Y} = \mu_X + \mu_Y\).