# GATE (TF) Textile 2021 Question Paper Solution | GATE/2021/TF/23

###### Question 23 (Textile Technology & Fibre Science)

If the sample size (n) is 25 and the standard deviation () of population is 2, then the standard error (SE) of sample mean, (rounded off to one decimal place), is __0.4___.

write here

Formula:
Standard error(SE)= where, is standard deviation and n is the sample size,
Given , =2 , n=25
so, SE= =2/ =2/5

### What is standard deviation ?

Standard deviation is a statistical measure that is used to describe the amount of variability or dispersion of a set of data from its mean or average value. It measures how much the individual data points deviate from the mean, on average. A higher standard deviation indicates that the data points are more spread out, while a lower standard deviation indicates that the data points are more clustered around the mean.

### How can you calculate standard deviation ?

To calculate the standard deviation, you can follow these steps:
Calculate the mean or average of the data set.
Calculate the difference between each data point and the mean.
Square each of the differences.
Sum up the squared differences.
Divide the sum of squared differences by the number of data points minus one.
Take the square root of the result obtained in step 5.
The formula for standard deviation is:
s = √[(Σ(xi – x)²) / (n – 1)]
Where: s = standard deviation Σ = sum of xi = each data point x = mean n = number of data points
There are also many software programs, such as Excel or statistical software, that can calculate the standard deviation for you.