In a particular study if the sample size was 50, then standard error was 8 units. How much would be the standard error if sample size was increased to 200?

Question

Question

This question was previously asked in

SSC CGL Tier-II ( JSO ) 2017 Official Paper ( Held On : 22 Feb 2018 )

Answer 1

Given

n = 50

S = 8

n = sample size

S = Standard deviation

Formula

S = ρ/√n

Calculation

We know that from the upper formula, ρ = S√n

⇒ 8 × √50

According to the question, if the sample size increased by 200

⇒ new n = 200

⇒ Standard error = ρ/√n

⇒ (8 × √50)/√200

⇒ 4

∴ The standard error is 4 if sample size was increased to 200.
Additional Information

Standard Deviation (S. D):
- A standard deviation denoted by σ is a measurement of the spread of a dataset around its mean.
- Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
Standard Error (S. E):
- The standard error of the mean, or simply standard error, indicates how different the population mean is likely to be from a sample mean.
- It tells you how much the sample mean would vary if you were to repeat a study using new samples from within a single population.