Question

opal is collecting data on water levels in different parts of town. she notices that her sample data has a low - value outlier. which statement must be true?

• removing the outlier will not change the spread of the graph of the data set.
• removing the outlier will not change the variance of the data set.
• removing the outlier will increase the variance of the data set.
• removing the outlier will decrease the spread of the graph of the data set.

Explanation:

Step1: Recall Outlier Impact

An outlier (low - value here) is a data point far from most others. Spread (e.g., range, IQR - related spread) and variance (measure of data spread around mean) are affected by outliers.

Step2: Analyze Each Option

• Option 1: Removing a low - value outlier will change the spread (e.g., range = max - min; removing min (outlier) will decrease range). So this is false.
• Option 2: Variance depends on how far data is from mean. A low - value outlier is far from mean, so removing it will decrease variance. So this is false.
• Option 3: Removing a low - value outlier (which is far from the mean and increases the spread) will make data closer together, so variance will decrease, not increase. False.
• Option 4: The low - value outlier makes the data spread out more (e.g., range is larger because of the small outlier). Removing it will make the data points closer together, so the spread of the graph (like range, or the visual spread in a plot) will decrease. True.

Answer:

Removing the outlier will decrease the spread of the graph of the data set.