The standard error of the mean is the standard deviation of sample means.

The standard error of the mean (SEM) is a measure of the precision of the sample mean as an estimate of the population mean. It is calculated as the standard deviation of the sample means divided by the square root of the sample size.

Explanation:

To fully understand the answer, let's break down the explanation into the following sections:

1. Standard error of the mean (SEM):
- The standard error of the mean is a statistical term that quantifies the amount of variability or dispersion in the sample means.
- It is often denoted as SEM and is calculated by dividing the standard deviation of the sample means by the square root of the sample size.
- The SEM provides an estimate of the precision or accuracy of the sample mean as an approximation of the true population mean.
- In other words, it tells us how much we can expect the sample mean to deviate from the true population mean.

2. Standard deviation (SD):
- The standard deviation is a measure of the dispersion or spread of a set of values.
- It quantifies the average amount by which each value in the data set differs from the mean.
- The SD is calculated by taking the square root of the sum of squared deviations from the mean, divided by the number of observations minus one.

3. Sample means:
- When we take multiple samples from a population and calculate the mean of each sample, we obtain a distribution of sample means.
- These sample means will vary from sample to sample due to random sampling variability.
- The distribution of sample means is centered around the true population mean and follows a normal distribution if the sample size is large enough.

4. Relation between SEM and SD:
- The SEM is directly related to the SD of the sample means.
- As the sample size increases, the SEM decreases because the sample means become more precise estimates of the population mean.
- The SEM is equal to the SD divided by the square root of the sample size.

5. Correct answer:
- In the given question, the correct answer is option 'C' - mean.
- The standard error of the mean is specifically calculated based on the standard deviation of the sample means, not the median or mode.
- The mean is a measure of central tendency that represents the average value of a set of observations.
- Therefore, the correct answer is the mean.