Normally we come across the word deviation in our daily life. Example: Deviation of the compass needle, road deviation, etc. Here the deviation indicates the change of path or direction. Similarly, in statistics, standard deviation shows how much the numbers have deviated from the mean. If the values of the mean will deviate more the value of standard deviation will be more. The Greek letter ‘sigma’ is used to denote the standard deviation, that is . This is a really interesting topic and is important to understand. Cuemath live math classes help you to understand such crucial topics in a simple way. They make it interactive and engaging to help you learn it thoroughly.
What Is Statistics?
The science of collecting, analyzing, presenting, and interpreting data is referred to as statistics. It is very handy while handling population data, economic data, etc. Currently, the medical field is extensively using it for handling the vaccination data. It’s an application of various methods to collect and analyse the data arranged in a particular series. Measures of central tendency and measures of dispersion are the basics of statistics and include mean, median, mode, etc.
- The average of all the observations collected when arranged in a series is mean.
- Whereas to know the median of the observations, you need to place them in a series and take the central value.
- Mode is the observation that occurs frequently in the series.
Let us learn how to determine the standard deviation of various data sets and then we will learn more about statistics and data.
Definition and Formula of Standard Deviation
Standard deviation is defined as the measure of finding the dispersion of a dataset relative to its mean. You can evaluate it by calculating the square root of the variance. It is mainly used in statistics.
There are two formulas to find the standard deviation. They are
1. The ‘population standard deviation’: = 1Ni = 1N(xi-)2
Where xi = individual x values
N = Total number of values and = The population mean
2. The ‘sample standard deviation’: s = 1N – 1i = 1N(xi-x )2
Where x shows the a.m of the values
The important change in sample standard deviation is “N-1” instead of “N” (which is called “Bessel’s correction”).
Steps to Calculate Standard Deviation
1. Calculate the A.M of the values.
2. Calculate the squared differences from the mean. (The data value – mean)2
3. Find the variance. Where the variance is the average of the squared differences from the Mean (Variance = 1Ni = 1N(xi-)2)
4. Find the square root of variance. (Standard deviation = Variance)
Few Examples of Uses of Statistics
- It is used to evaluate the marks scored by the students in a class having a total of 40 kids. The mean value is the statistical value of the score obtained.
- It is also used to find the total number of members who are going to attend the rally out of the total number of people living in the city.
- To measure the correlation coefficient
- To calculate skewness
- It is used in Geology, weather forecasting
Role of Data in Statistics
Statistics is all about collecting and analyzing data to measure results. Statistics involve two types of data. One is qualitative data and quantitative data. The former is known as descriptive data. For example, if you see a boy running fast, it is descriptive. If you say you have 10 fingers, it is quantitative data as it has a number in it. A data in statistics can be represented in many forms like
- Bar Graph
- Line graph
- Pie Chart and so on