Final Answer:
The standard deviation of a sample is the square root of its variance. Given that the variance of the sample is 16, the standard deviation is √16 = 4. Therefore, option A) 4 is the correct choice.
Step-by-step explanation:
The standard deviation (σ) is the square root of the variance (σ²) and is represented as σ = √σ². If the variance of a sample is 16, it implies that σ² = 16. Taking the square root of 16, we get σ = √16 = 4. Therefore, the standard deviation of this sample is 4.
The standard deviation measures the dispersion or spread of data points within a dataset. It quantifies the average distance of each data point from the mean. A higher standard deviation signifies greater variability among the data points. In this case, a standard deviation of 4 indicates that the data points in the sample are, on average, 4 units away from the mean.
Understanding the relationship between variance and standard deviation is crucial in statistics. Variance is a measure of the average squared deviations from the mean, while the standard deviation is a measure of the typical distance between each data point and the mean. Calculating the standard deviation from the variance helps in understanding the variability and distribution of data within a sample. Therefore, in this scenario, with a variance of 16, the corresponding standard deviation is 4.option A)