The Standard error of mean is calculated on the basis of ___________.

A. Grand Mean

B. Size of the sample

C. Sample standard deviation

D. Sampling distribution of mean

E. Population mean

Choose the correct answer from the options given below: 

The correct answer is Option 2: B and C only.

Important Points

The standard error measures how much the sample mean is expected to vary from the true population mean. It takes into account the sample size and sample standard deviation— It's a key concept in understanding the reliability of sample statistics.

 Grand Mean:

• The grand mean is the mean of means from different samples.
• It is not directly used in calculating the standard error of the mean.

 Size of the Sample:

• The size of the sample (sample size) directly affects the standard error of the mean.
• As the sample size increases, the standard error tends to decrease.
• This is because larger sample sizes provide more reliable estimates of the population mean.

Sample Standard Deviation:

• The sample standard deviation is used to quantify the spread or dispersion of data within a sample.
• It is a crucial component in calculating the standard error of the mean.
• The formula for the standard error of the mean involves dividing the sample standard deviation by the square root of the sample size.

 Sampling Distribution of Mean:

• The standard error of the mean accounts for the variability in the sampling distribution of the mean.
• However, it is not directly calculated based on the sampling distribution itself.

 Population Mean:

• The population mean is not directly used in calculating the standard error of the mean.
• The standard error focuses on the variability of the sample mean as an estimate of the population mean.

In summary, the correct options are B and C because the standard error of the mean is influenced by the sample size (B) and the sample standard deviation (C).