One of the most common and basic methods to find various values in statistics can be defined as the standard deviation formula. It can also be regarded as the square root of the variance. The standard deviation is mostly abbreviated as SD which also tells how the mean formula has deviated. The standard deviation formula and the mean formula are quite related. Mean can be defined as one of the types of central measures of tendency which helps to find the average or central score for a given data or observation. If the standard deviation is low, then it is close to the mean and if it is high, then it signifies that the standard deviation is far from the mean. This formula is widely used in the sample of a population, probability, various other data, and so on. In this article, we will try to cover some basic aspects regarding the standard deviation formula such as steps of calculating and important points to remember and do a detailed analysis about it.
What is Mean?
As mentioned above, mean can be defined as one of the types of central tendency of measures that helps to find the average or mean value of a data or observation. For example, if you scored 35, 45, 65 in your examination, to find the average value you need to know the mean formula. The mathematical formula given for mean is the sum of all observations divided by the total amount or number of observations. Let us try some examples so that you understand this concept in a better way.
Example 1: Calculate the mean for the observation, if the given observations are as follows: 5, 9, 3, 2?
Solution: Given that,
Total number of observations = 4
When arranged in increasing order = 2, 3, 5, and 9.
Using the formula of mean = sum of observation / total number of observations.
2 + 3 + 5 + 9 / 4 = 4.75.
Therefore, the mean of the given observation is equivalent to 4.75.
Example 2: Calculate the mean of the first five even numbers?
Solution: Given that,
We already know that the first five even numbers according to the number line are = 2, 4, 6, 8, and 10.
Total number of observations = 5
Using the formula of mean = sum of observation / total number of observations.
2 + 4 + 6 + 8 + 10 / 5 = 6
Hence, the mean of the first five even numbers is equivalent to 6.
Steps of Applying the Standard Deviation Formula
The following points analyze the steps of applying the standard deviation formula:
- The first step is to calculate the arithmetic mean of the given observation.
- The second step is to find the squared differences and average differences of the mean.
- Finally, find or calculate the square root of the given variance using the formula.
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