The ________ represents the number of standard deviations an observation is from the mean.

Verified step by step guidance

1. Identify the concept described: it refers to how far an observation is from the mean in terms of standard deviations.
2. Recall that in statistics, the measure that expresses the distance of a data point from the mean in units of standard deviation is called a 'z-score' or 'standard score'.
3. Understand that the z-score is calculated by subtracting the mean from the observation and then dividing by the standard deviation.
4. Write the formula for the z-score as: \(z = \frac{X - \mu}{\sigma}\), where \(X\) is the observation, \(\mu\) is the mean, and \(\sigma\) is the standard deviation.
5. Recognize that the z-score helps to standardize different data points, allowing comparison across different distributions.

Key Concepts

Standard Deviation

Standard deviation measures the amount of variation or dispersion in a set of data values. It quantifies how spread out the observations are from the mean, with a higher standard deviation indicating more variability.

Mean

The mean is the average of all data points in a dataset, calculated by summing all values and dividing by the number of observations. It serves as a central reference point for measuring deviations.

Z-Score

A z-score indicates how many standard deviations an individual observation is from the mean. It standardizes data points, allowing comparison across different datasets by showing relative position within the distribution.