Standard Deviation Calculator

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In today’s world the daily data generating is enormous. Getting insights and analyzing it is crucial and important task. Here standard deviation definitely become useful. In this article calculation of standard deviation is explained.

standard deviation calculator

Standard deviation, often relegated to the realm of statistics textbooks, plays a surprisingly significant role in our daily lives. This seemingly complex concept acts as a practical tool for understanding the variability in various data sets, offering valuable insights across diverse scenarios.

Standard Deviation represents the spreadness of data, or dispersion of values in data relative to mean of the data. It is a measure of how each number is observed from the mean.

Standard deviation is a important tool in statistical and probabilistic analysis. Alone it is not sufficient to finding results and used along with other statistical tools. In this article automatic standard deviation calculator is included, which is helpful for students, engineers and data analysts.

Square of Standard deviation is called Variance. It helps measure how far the data has spread out. Concept of standard deviation applies only when data follows normal distribution. We can say data graph is in bell shape.

Formula of standard deviation

    \[ \sigma = \sqrt{\frac{\sum_{i=1}^{n}{(x-\bar{x})^2}}{N}} \]

standard deviation of sample and population
population vs sample

In Statistics the statistical operations on whole data and a portion of it handled differently. Here comes the concept of sample and population. Complete or whole data is called as population i.e. the data which we are trying to analyse and make conclusions out of it. Part of the whole data is the sample.

How to calculate standard deviation using standard deviation calculator:

  • Calculate mean of the data. For this add all values in data and divide by size of data.
  • Subtract mean from every value and square the each resultant value, then sum all.
  • Divide the final value with size of data (N). If partial data is taken for calculation, then divide final value with size of data taken minus one (n-1) instead of N.
  • Then apply square root, it is the standard deviation of the data.

By knowing the standard deviation one can get idea of the variation that is normal or drastic. Standard deviation used in the process of identifying the outliers of data i.e. unusual instances of data.

Standard Deviation Example

Students Marks in a Class

Calculating standard deviation of marks obtained by students in a class, who attend a exam. All marks are listed below in ascending order. No. of students in the class is 12. Maximum marks are 100, Pass marks are 50.

students in class standard deviation

List of Marks: 31, 42, 54, 56, 57, 63, 67, 75, 76, 82, 86, 91

Mean or average: 65

Subtract average from each data value
31-65, 42-65, 54-65, 56-65, 57-65, 63-65, 67-65, 75-65, 76-65, 82-65, 86-65, 91-65
-34, -23, -11, -9, -8, -2, 2, 10, 11, 17, 21, 26

Square all values
1156, 529, 121, 81, 64, 4, 4, 100, 121, 289, 441, 676

Sum above numbers

Divide by total no of data values

Square root of above value

Std: 17.28

Graph Representation

standard deviation calculation graph
Mean and Upper and Lower Standard Deviation lines

Lower and Upper standard deviation limits:

47.71, 82.28

0 —47.71 — 65 — 82.28 — 100


Standard deviation of 17 marks tells that students performance varies significantly.
Lower standard deviation spanned below into pass mark limit.

The above procedure can be used to calculate standard deviation manually or use online calculator in this page for quick calculation.

General Applications of Standard Deviation

In the world of business, standard deviation helps us analyze sales fluctuations, inventory management, and customer behaviour. By calculating the standard deviation of sales figures, businesses can identify periods of high or low activity, allowing for better resource allocation and strategic planning. Similarly, tracking inventory deviations helps minimize stockouts and overstocking, ensuring optimal efficiency. Furthermore, standard deviation aids in understanding customer behaviour, such as analyzing purchase patterns and identifying products with high variability in demand.

Beyond the realm of business, standard deviation finds application in our day-to-day activities. Imagine planning a potluck with friends. By calculating the standard deviation of the estimated number of attendees from each guest, you can get a better sense of the potential range of participants, allowing for more accurate food preparation. Similarly, while baking, standard deviation helps ensure consistency in your measurements. By understanding the typical variation in ingredient weights from recipe recommendations, you can adjust your measurements accordingly, leading to more consistent baking results.

The applications of standard deviation extend even further. In education, it helps assess student performance by understanding the spread of scores in a class. In sports, it assists in analyzing player performance consistency and identifying areas for improvement. Even in weather forecasting, standard deviation plays a role in understanding the typical variation in temperatures and precipitation.

Understanding standard deviation empowers us to extract valuable information from the data surrounding us. It acts as a silent but powerful tool in navigating the world around us, making informed decisions in business, planning for daily activities, and even gaining insights into the natural world. So next time you encounter data with inherent variability, remember the power of the standard deviation.

Analysing Monthly bills by Standard Deviation

One can calculate the standard deviation of your monthly bills using this standard deviation calculator. Input all the bill amounts of every month of the year in the above calculator and click submit. This value provides you with insights into the variability of your spending throughout the year. A high standard deviation indicates that your monthly bills fluctuate significantly, whereas a low standard deviation suggests more consistent spending patterns.