Question

abby is collecting rainfall data. she finds that one value of the data set is a high-value outlier. which statement must be true?

abby will use a different formula for calculating the standard deviation.
the outlier will increase the standard deviation of the data set.
the spread of the graph of the data will not change.
abby will not use the mean when calculating the standard deviation.

Explanation:

Analyze the effect of an outlier on standard deviation

Using the Outlier Effects on Statistics knowledge point

An outlier is a data point that is significantly far from the rest of the values in a data set. Standard deviation measures the average distance of each data point from the mean. Because an outlier lies far from the mean, its squared deviation from the mean is very large, which increases the overall variance and standard deviation of the data set.

Evaluate the given options

Using the Outlier Effects on Statistics knowledge point

• Option 1: "Abby will use a different formula for calculating the standard deviation."

This is false. The standard formula for standard deviation is used regardless of whether outliers are present.

• Option 2: "The outlier will increase the standard deviation of the data set."

This is true. Outliers increase the variability or spread of a data set, thereby increasing the standard deviation.

• Option 3: "The spread of the graph of the data will not change."

This is false. An outlier increases the overall spread of the data.

• Option 4: "Abby will not use the mean when calculating the standard deviation."

This is false. The mean is a fundamental component of the standard deviation formula.

Answer:

• Abby will use a different formula for calculating the standard deviation.
• The outlier will increase the standard deviation of the data set. (Correct answer)
• The spread of the graph of the data will not change.
• Abby will not use the mean when calculating the standard deviation.