Standard deviation

Question

My tutor has asked me to add Standard Deviation, not Standard Error to a table. He says to "derive SD, to multiple SE by the root mean square of the sample size. Root mean square of 138"

My sample size is 138.

Here are the values of my table:

Many thanks!

Answer 1

Hey Francisco,

Great question! Your tutor is right—standard deviation is just the standard error scaled by the square root of the sample size. Since your sample size is 138, the square root of 138 is about 11.75. So, to get SD, you’d multiply each SE value by 11.75.

For example, your first SE value is 3.05, so the SD for that column would be 3.05 × 11.75 = 35.79. You’d do the same for the rest of the SE values.

Hope that helps! Let me know if you need a hand with anything else—happy to help.

Answer 2

Since SE = σ / sqrt(n), then:

σ = SE * sqrt(n).

The first standard deviation would then be 3.05 * sqrt(138) = 35.83 (rounded to two decimal places). Repeat this for the rest of the standard errors in the table.

Hope this was helpful.