Question

The standard deviation of a sample of 100 observations equals 64. the variance of the sample equals:

Answer 1

The variance of the sample is 4096, obtained by squaring the standard deviation, which is 64.

Step-by-step explanation:

The question asks for the variance of a sample when the standard deviation is known to be 64. The variance of a sample is the square of the sample standard deviation. Therefore, to find the variance, we simply square the standard deviation. Since the standard deviation is 64, the variance is calculated as follows:

Variance =
`Standard Deviation^(2)` =
`64^(2)`= 4096.

This numeric outcome, 4096, signifies the variance of the sample. It serves as a quantitative representation of the dispersion within the dataset, shedding light on the extent to which individual data points deviate from the mean.

By delving into the intricacies of variance, we gain a deeper understanding of the variability inherent in the sample, a crucial aspect in statistical analysis and inference.

Answer 2

In general we know standard deviation is a measure of how the numbers are spread out.

And variance is the average of squared difference from mean.

So the relation between variance and standard deviation is as given below:

Standard deviation is the square root of variance.
So we can say variance is the whole square of standard deviation.

In given question standard deviation is 64.

So the variance will be square of 64.
Variance =
`(64)^2`
=
`64*64 = 4096`
So the variance of given 100 observation is 4096