What is Sample Mean Formula? Standard Error Of The Sample Mean Formula


What is Sample Mean?

As we know, sample is just a small part of the whole. For example, if you wanted to know how much people generally pay on food per year, then you should take a poll over 300 million people here. In simple words, take a fraction is 300 million people here the fraction is sample. The other common word for the Mean if average here. Here, we could say that sample mean is the average amount that is paid by thousand of people on food every year.

Calculate Sample Mean

It is useful calculating sample mean in statistics because it allows you estimating what the whole population is doing. For example, if you have calculated an average or sample mean for the people spending on food every year i.e. $2400 per year then the value would be same even if you are taking the population as a whole. So, its better work on samples instead of taking the population or anything else as a whole.

Sample Mean Formula

 It will be less time consuming and taking less resources too. So, sample mean could save a lot of money in your case. The process looks complicated but this is quite easy and flexible in understanding. Remember the concept of average calculation in the basic mathematics. The things are perfectly same here too, only the notation or we could symbols are different. To understand Sample Mean formula, let us break it down into pieces as given below-

\[\large \overline{x}=\frac{\sum_{i-1}^{n}x_{i}}{n}\]

Where,
$\bar{x}$ = sample mean
\sum_{i=1}^{n}x_{i} = x1+x2+….+xn
n = Total number of terms
x1, x2…….xn are different values.

Now, you just have to plugging values and solve them arithmetically or you could use calculators too in advanced cases.

Question 1: The total marks obtained by few students in mathematics exam are 101, 161, 155, 96 and 83. Evaluate the sample mean marks ?

Solution:
Mean \[\ \bar{x} = \frac{\sum_{i=1}^{n}x_{i}}{n} \] Total number of terms(n) = 5
Mean = \[\ \bar{x} = \frac{101 + 161 + 155 + 96 + 83}{5} \]
= 119.2


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