A random sample of 80 students at a largae school shows an average grade of 72 in Algebra with a standard deviation of 4. Find the standar error.

SEm = SD/√n

Insert values and calculate.

To find the standard error, you first need to understand that it measures the variability or dispersion of the sample mean. It quantifies the accuracy with which the sample mean represents the population mean. The formula for standard error is:

Standard Error = (Standard Deviation) / √(Sample Size)

In this case, the standard deviation (σ) is given as 4, and the sample size (n) is given as 80. Thus, you can substitute these values into the formula to find the standard error.

Standard Error = 4 / √(80)

Now, simplify the square root:

Standard Error = 4 / √(8 * 10)

Since √8 is 2√2, you can further simplify the expression:

Standard Error = 4 / (2√2√10)

Now, you can simplify by multiplying the √2 and √10:

Standard Error = 4 / (2 * √(2 * 10))
Standard Error = 4 / (2 * √20)

Since √20 is 2√5, you can further simplify the expression:

Standard Error = 4 / (2 * 2√5)
Standard Error = 4 / (4√5)

Finally, divide both the numerator and denominator by 4:

Standard Error = 1 / √5

Therefore, the standard error is 1/ √5 (or approximately 0.447).