Final answer:
The variance of the sample is calculated by squaring the standard deviation. With a given standard deviation of 49, the variance is 49 squared, which equals 2401 (option c).
Step-by-step explanation:
The student's question is regarding the calculation of variance from the standard deviation for a sample of observations. Since the variance is the square of the standard deviation, we need to square the given standard deviation value to find the variance.
If the standard deviation of a sample of 81 observations is 49, to calculate the variance, we square the standard deviation:
Variance = (Standard Deviation)2
Variance = 492
Variance = 2401
Therefore, the variance of the sample is 2401, which aligns with option c.