Standard deviation is a measure of:a. rangeb. central tendencyc. inferenced. dispersion

Break Down the Problem

1. Identify what standard deviation measures in statistics.
2. Examine the options to determine which one aligns with the definition of standard deviation.

Relevant Concepts

• Standard deviation quantifies the amount of variation or dispersion in a set of data values. A low standard deviation indicates that the data points tend to be close to the mean, while a high standard deviation indicates that the data points are spread out over a wider range of values.

Analysis and Detail

1. Range: Refers to the difference between the highest and lowest values in a set of data. It is not a measure of how individual data points vary from the mean.
2. Central Tendency: This includes measures like mean, median, and mode, which represent the center of a data distribution, not the spread or dispersion.
3. Inference: Involves making predictions or generalizations about a population based on sample data. Standard deviation does not directly measure inference.
4. Dispersion: Represents how far the data points are spread out from their mean. This aligns directly with what standard deviation measures.

Verify and Summarize

After analyzing the options, it is clear that standard deviation specifically measures dispersion in a data set.

Final Answer

d. dispersion