##### Asked by: Carmella Pflugelbauer

asked in category: General Last Updated: 30th April, 2020# Which data set has the smallest standard deviation?

**smallest**possible

**standard deviation**for any

**set**is 0, and the

**standard deviation**of a

**set**will be zero when all the

**data**points are the same.

Besides, what is the smallest standard deviation?

The **smallest standard deviation** possible in a distribution is 0. This occurs when each element of the distribution is the same. A **deviation** is a data point's distance from the distribution mean. If all points in the distribution are the same, then the mean is the same as each distribution point.

Similarly, which data set has largest standard deviation? As we can see, the **data** values from **set** D are the farthest from its mean out of all the **data sets** (four of its 5 values, -50, 33, 34, and 35, are farther from 10 than any values in the other **data sets**); thus, **set** D **has** the **greatest standard deviation**.

Likewise, how do you know if standard deviation is small or large?

The center of the graph is the mean, and the height and width of the graph are **determined** by the **standard deviation**. When the **standard deviation is small**, the curve will be tall and narrow in spread. When the **standard deviation** is **large**, the curve will be short and wide in spread.

What is an example of when you would want consistent data and therefore a small standard deviation?

**Example** of the situation when **we want data** to be **consistent**, and **therefore, a small standard deviation** is the positive performance of a cricketer. **Example** of the situation when **we want data** to have large **standard deviation** is the quality score of the rival's product.