 In coming slides, we will discuss about standard deviation and confidence interval. Standard deviation is a very important concept, which is used to measure the precision, i.e. closeness of data. Closeness of data to the actual value is called accuracy, while closeness of data within itself is called precision. So, we measure the precision through standard deviation. The formula used for standard deviation is this standard deviation, which we are dividing from n. So, you must have understood that this is being used for population standard deviation. That is why the population mean or mu is represented here. There are x i individual readings and we will incorporate all the data from 1 to n in this. When we calculate from the excel sheet, instead of n, we calculate with n-1. And we calculate the sample standard deviation. How do we calculate it? We do it stepwise. Through a few commands in the excel sheet. But to understand this formula, for example, we have individual readings like 81, 83, 80. And if their mean is calculated, then we will collect these 7 readings and divide them from 7. Our mean value is 81. So, we write this mean with all these, 81. We will minus every reading from this mean. Now, some of your readings will also come in minus. Minus 2, minus 2, minus 3. If it is exactly equal to the mean, then 0 will also come. If your individual reading is more than the mean, then your reading will also come in positive. But when their square will be taken, then all these negative and positive readings will be in positive form only. After this, we will sum all these values, whose sum is 22. And n-1, i.e. our 7 readings, then we divide it from 6 instead of 7. If we round off 3.6, then approximately 4 answer will come. And for standard deviation, I have to take under root of this 4, after which my standard deviation value is 2. When we report the results, then basically mean plus minus standard deviation is the way to report. i.e. the data I have, its maximum value is 83 and minimum value is approximately 79. You can observe that some values are exactly the same as this, some values are less than this. My main data will be covered between this expanded form, i.e. 79 to 83, approximately all the data is present. Confidence interval. Basically, a Gaussian curve, which we have observed earlier, how much data is being covered in it, we will call it confidence interval. In this Gaussian curve, the main portion, i.e. 68%, it only lies between plus minus once time standard deviation. i.e. 68% chances, which I have calculated in the standard deviation by applying formulas, then if 81 plus minus plus 2 and minus 2, then my maximum data will be lying between this. 68% chances is that the data will be lying in this portion. If I consider 2 times standard deviation i.e. 81 plus 4 and 81 minus 4, then chances are that my 95% data will be between this confidence interval. i.e. if I increase the values of the data, then the remaining values will also come between it. And if we add or subtract it from 3 times standard deviation, then approximately 99% data is covered in it. These values i.e. 68%, 95% or 99% is the confidence interval. i.e. 1 times standard deviation i.e. plus minus with the mean value, then 68% chances are that your data will be lying between this. And between 2 times standard deviation plus minus, your 95% data and between 3 times standard deviation, your 99% data will be lying. Right now, we have only experimented with 7 readings. When our readings are in 5 km, then this standard deviation gives us very important information.