Standard Deviation Formula

Q1

What is the standard deviation?

For a set of data, the measure of dispersion, about mean, when expressed as the positive square root of the variance, is called standard deviation.

Q2

What is the standard deviation formula?

Standard deviation formula is given by the root of summation of square of the distance to the mean divided by number of data points.

σ = √(∑(xi – μ)²/N)

Here,
σ = Population standard deviation
N = Number of observations in population
x_i = ith observation in the population
μ = Population mean

Q3

How to calculate the standard deviation?

To calculate the standard deviation, follow the following steps:
Step 1: Calculate the mean of given data points
Step 2: For all the points, find the square of the distance to the mean
Step 3: Find the sum of all the squared terms
Step 4: Divide the whole by the number of data points
Step 5: Find the square root

Q4

Find the mean using the following data set.
5, 10, 15, 20, 25

Given: 5, 10, 15, 20, 25

Number of data values = N = 5

Mean = (5 + 10 + 15 + 20 + 25)/5 = 15

Q5

What is the formula for variance?

Variance is the square of the standard deviation i.e., Variance = σ²