If all observations in a dataset are close to the mean, what does this indicate about its variance?

If all observations in a dataset are close to the mean, what does this indicate about its variance?

• A. The data has large variance
• B. The data exhibits small variance
• C. The variance is not applicable
• D. The data points are heterogenous

Answer: (B)

When all observations in a dataset are close to the mean, this indicates that the data points are clustered tightly around the average value. Variance is a statistical measure that represents the degree to which each data point differs from the mean. If the observations are closely grouped, it means that there is little deviation from the mean, leading to a smaller variance. A small variance signifies that the values in the dataset do not spread out widely but remain fairly consistent. This uniformity contributes to the conclusion that the variability of the dataset is minimal. Consequently, when the data points are tightly packed around the mean, it corroborates the assertion of having a small variance, confirming that the data is relatively consistent.

When all observations in a dataset are close to the mean, this indicates that the data points are clustered tightly around the average value. Variance is a statistical measure that represents the degree to which each data point differs from the mean. If the observations are closely grouped, it means that there is little deviation from the mean, leading to a smaller variance.

A small variance signifies that the values in the dataset do not spread out widely but remain fairly consistent. This uniformity contributes to the conclusion that the variability of the dataset is minimal. Consequently, when the data points are tightly packed around the mean, it corroborates the assertion of having a small variance, confirming that the data is relatively consistent.