What does a high variance indicate about a dataset?

What does a high variance indicate about a dataset?

• A. The data points are closely clustered around the mean
• B. The data points are widely dispersed from the mean
• C. The data has outliers affecting the mean
• D. The data is perfectly correlated

Answer: (B)

A high variance in a dataset is indicative of the data points being widely dispersed from the mean. Variance itself is a measure of how far each number in the set is from the mean and from every other number. When the variance is high, it suggests that the values are not tightly packed and that there is a greater degree of variability. This means that some data points are significantly higher or lower than the mean, leading to a broader spread of values across the dataset. In contrast, a low variance would suggest that the data points are more clustered around the mean, leading to less overall variability. The presence of outliers might affect variance but does not solely define it; rather, high variance reflects the general distribution pattern of all data points relative to the mean. Correlation refers to a relationship between two variables and does not pertain to the concept of variance in a single dataset. Thus, the conclusion from recognizing high variance is that the data points diverge widely from the average value.

A high variance in a dataset is indicative of the data points being widely dispersed from the mean. Variance itself is a measure of how far each number in the set is from the mean and from every other number. When the variance is high, it suggests that the values are not tightly packed and that there is a greater degree of variability. This means that some data points are significantly higher or lower than the mean, leading to a broader spread of values across the dataset.

In contrast, a low variance would suggest that the data points are more clustered around the mean, leading to less overall variability. The presence of outliers might affect variance but does not solely define it; rather, high variance reflects the general distribution pattern of all data points relative to the mean. Correlation refers to a relationship between two variables and does not pertain to the concept of variance in a single dataset. Thus, the conclusion from recognizing high variance is that the data points diverge widely from the average value.