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### Standard error of the mean

• date 4th July, 2019 |
• by Prwatech |

# Standard error of the mean tutorial

Standard error of the mean tutorial, Are you the one who is looking for the best platform which provides information about Standard error of the mean towards data science? then welcome to the land of Standard error of the mean tutorial used in statistics. Before proceed, we recommend you to go through our previous blog in this series on need of sampling distribution of the sample mean in data science.

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## Standard error of the mean Definition

The standard error is a method used to estimate the approximate standard deviation of a sampling distribution.

Sampling Distribution

The Sampling Distribution is the mean of the population from where the items are sampled. If the population distribution is normal, then the sampling distribution of the mean is likely to be normal for the samples of all sizes.

Suppose there are 1000 girls in a school and we are supposed to find the average height of these girls.

If we take random a set of 20 girls from the population measure their heights and find its mean as x̅1. Then we take another random set of 20 girls from the population and measure their heights and find its mean as x̅2.

Similarly, if took 20 such sets randomly and finds their means as

123 – – – – x̅20

### Standard error of the mean formula

Where: σ = standard deviation of the original distribution

N =Sample Size

σm= Standard Error.

### Why we need Standard error of the mean?

Standard error plays a very important role in the large sample theory. It forms the basis for the testing of a hypothesis.

The statistical inference involved in the creation of confidence interval is mainly on the basis of standard error.

The magnitude of standard error indicates an index of the precision of the estimate of the parameter. Standard Error is inversely proportional to the sample size, i.e. that a smaller sample size tends to produce greater standard errors.

### Standard error of the mean Example

 Name Jack John Jonny Jaaz Weight (in kg) 72 74 78 84

Now find the Deviation

 Name Jack John Jonny Jazz Weight (in kg) 72 74 78 84 Deviation 72-77 = -5 74-77 = -3 78-77 = 1 84-77 = 7

Now perform squares of all the Deviations

 Name Jack John Jonny Jazz Weight (in kg) 72 74 78 84 Deviation 72-77 = -5 74-77 = -3 78-77 = 1 84-77 = 7 Square of Deviation 25 9 1 49

Now find Standard Deviation by taking a mean of Square of Deviations:

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