 Dear students, we talked about the range, interquartile range and mean deviation in the last module. And in this module, we are going to discuss about the variance and standard deviation. What is the variance? Variance is the average of the square differences from the mean. When we read the mean deviation, we read the mean deviation as an assumption of the x minus x bar is always zero, i.e. when we sum the mean deviation, the sum of x bar is zero. So, instead of mean deviation, we consider variance to be a better measure to calculate the variance because in this, we take the square of your deviation and divide it from the total number. So, we call the under root of variance as standard deviation. So, the square root of the deviation is the square root of the variance. Standard deviation, we can compute with two formulas. One is the simple formula, the second formula is called the RASCORE method. You can use it in detail in the course of the statistics and learn how to compute it manually. So, the value we calculate for the standard deviation from these formulas, it is less in direction, it is plus minus on both sides. So, when we compare it with the relative dispersion of the arithmetic mean, we will see both sides. This one-sided dispersion does not tell us. The procedure for doing this in SPSS is that you will go to analyze, go to descriptive statistics, and from there you will click on the frequency and then you will select your variables and along with the central tendency, you will be given all the dispersion of the mayors. So, you will select them from here and continue. So, you will get a table like this in the output sheet. Which will tell you what is the information of the dispersion of the mayors. For example, here I have shared a variable of age and GPA in front of you. So, we know that we have the ground of age, which is 21, and there is standard deviation 2, and there is variance 4, range 11, minimum value is 18, and maximum value is 29. So, this data set tells us that overall, the dispersion is less because the value is 11, which is not too much because the midpoint of age, which we have calculated from the arithmetic mean, is 21. In this data set, which is 21 years old, and this data is 18 years old, which is at least the age of the report, and the age of the report is 39 years old, and with this midpoint, the value of the standard deviation is 2.063, which tells us that in this, dispersion, scatteredness is quite low. This data, the assumptions of normal distribution will not violate it, and it will not be very flattened, and it will not go towards too much torness. In the same way, we will learn how to calculate the kurtors in the distribution module, but we also get to know this from here, when we look at mean and standard deviation. Similarly, we have the mean of the GPA, which we have taken as a sample, and the average score of the students who participated in it, their average score is 3.23, and the minimum score reported in this is 1.50, and the maximum score reported in this is 4.0, which is a total 100% performance, and we have a passing mark in the semester system, 1.50, both are reported, and the standard deviation with 3.23 is 0.40, which means the majority of the data set is not that much varied, because we have a range of 2.50, so if we look at it in the context, then it is less than half a unit variation, so this variation is not that much, so what I have done here with the two variable compute from the data set, so there is not much dispersion or scatteredness in both, both are normally distributed data sets, so in the next module we will do some other variables with SPSS, we will do some exercises in it, and we will perform it again.