Which of the following best describes the usefulness of the $standarddeviation$ in statistics?

• A. It identifies the most frequently occurring value in a dataset.
• B. It calculates the $\frac{\sum x}{n}$ (sum of all data values divided by the number of values).
• C. It measures how much the data values deviate from the $mean$, indicating the spread or variability of a dataset.
• D. It determines the central value by arranging data in order and selecting the middle value.

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the concept of standard deviation. It is a measure that quantifies the amount of variation or dispersion in a set of data values.
2. Step 2: Recall that the mean is the average of the data, calculated by summing all values and dividing by the number of values.
3. Step 3: Recognize that the standard deviation measures how far each data point is from the mean, on average, which helps describe the spread or variability of the dataset.
4. Step 4: Differentiate standard deviation from other statistical measures: the mode identifies the most frequently occurring value, and the median is the middle value when data is ordered.
5. Step 5: Conclude that the standard deviation's usefulness lies in its ability to indicate the spread of data around the mean, helping to understand the consistency or variability within the dataset.