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March 29, 2024Standard Deviation And Variance: As per the definition of Standard Deviation in NCERT “the proper measure of dispersion about the mean of a set of observations is expressed as positive square-root of the variance and is called standard deviation. Therefore, the standard deviation, usually denoted by σ “. The formula for standard deviation is:
\(\sigma=\sqrt{\frac{1}{N}\sum_{i=1}^{n} (x_i-\bar x)^2}\)
Here we will provide you with all the details regarding Standard deviation such as the formula for ungrouped data, frequency distribution (discrete), frequency distribution (continuous), sample questions and other relevant information.
Mean Deviation, Variance, and Standard Deviation are topics from the Statistics chapter of Class 11 Maths. We have provided the formula for all 3 below based on the type of data set one is referring to:
The above formula will help you in your preparation and you can use these to prepare a formula sheet for revision purposes.
Here we will explain the step-by-step process to calculate the standard deviation along with calculating mean and variance.
Here is a solved example where you have to calculate only the SD (σ).
Example 1. Find the standard deviation for the following data:
\(x_{i}\) – 3, 8, 13, 18, 23
\(f_{i}\) – 7, 10, 15, 10, 6
Solution. Let us create a table for different values.
σ = \(\frac{1}{48}\) x 293.77 => 6.12.
Here are some questions that are mostly asked on the topic.
Q. How do you calculate the standard deviation? Ans. To calculate standard deviation follow the steps: Step 1: Find the mean for the given data set. Step 2: Calculate the variance (the formula is given on this page with a solved example). Step 3: Now, take the square root of the variance to find the value of σ. |
Q. What does Standard Deviation tell you? Ans. σ or SD tells us how far is the mean from each observation. |
Q. What is the standard deviation and variance? Ans. Variance estimates the average degree to which each observation differs from the mean and SD is the sqrt of variance. |
Q. What is the standard deviation example? Ans. Let say a data set is given with values 2, 1, 3, 2, 4. The mean and the sum of squares of deviations of the observations from the mean will be 2.4 and 5.2, respectively. So, σ will be √(5.2/5) = 1.01. |
Q. What is the use of standard deviation? Ans. It is used to estimate how a group of observations (i.e., data set) are spread out from the mean (average or expected value). |
That was all on Standard Deviation, we hope the information provided by us was helpful. However, if you have further questions feel free to use the comments section and we will provide you with an update.