Statistics is the branch of mathematics that deals with the study of the interpretation, analysis, presentation, collection, and organization of data. We can say that it is a mathematical discipline to collect, summarize data. Statistics is an important topic for the JEE exam. Through proper preparation and planning, students can easily crack this exam. They can easily score marks from statistics, if they learn the topic in the right manner.
Variance is a measure of central dispersion. It is denoted by σ2. It is given as the average of the squared difference from the mean. The average of a given set of numbers is termed as the mean. Let us see how to find variance in statistics.
How to Calculate Variance?
The steps to calculate variance are given below.
- Find the mean of the given numbers.
- Subtract the mean and find the square of the difference, for each number.
- Find the average of the squared differences.
- The formula is given by σ2 = ∑(xi – x–)2/n, where n is the number of observations, x– is the mean and xi denotes the observations.
Let us have a look at an example to find the variance.
Given observations are 1, 5, 3, 7, 4. Find the variance of the given data.
Here n = 5
mean = (1 + 5 + 3 + 7 + 4)/5
∑(xi – x–)2 = (1 – 4)2 + (5 – 4)2 + (3 – 4)2 + (7 – 4)2 + (4 – 4)2
= 9 + 1 + 1 + 9 + 0
Variance σ2 = ∑(xi – x–)2/n
The answer is 4.
Another important topic in statistics is Standard deviation (S.D) that calculates the dispersion of a dataset relative to its mean. It is denoted by σ. S.D is considered as a useful tool in investing and trading strategies. There is a greater deviation within the data set, if the data points are away from the mean. So the higher the spread out the data, the more the standard deviation.
Properties of Standard Deviation
Following are some properties of standard deviation.
- D is never negative.
- It is used to calculate the spread or dispersion around the mean of a data set.
- Standard deviation is sensitive to outliers.
- The more the spread, the more the standard deviation, for data with approximately the same mean.
- When all the values of a data set are the same, the standard deviation is zero.
How to calculate variance from standard deviation
Standard deviation can be highly affected if the mean gives a poor measure of central tendency, since it is closely linked with the mean. S.D is an indicator of the presence of outliers. It is also useful when comparing the spread of two separate data sets that have almost the same mean. Let us discuss how to find variance from standard deviation.
If S.D (σ) is given, then find the square of standard deviation to get the variance. (S.D)2 gives the variance. Standard deviation is the square root of variance. Standard deviation and variance play important roles throughout the financial sector, including the areas of economics, accounting, and investing. These are useful and significant for traders, who use them to measure market volatility.