Well, with lecture 26, time has come to discuss about descriptive statistics. In this lecture, we will learn about the measures of dispersion and central tendency, constructing the frequency distribution and cumulative frequency distribution. I have been discussing about the central tendency during my previous lectures. Now, it is the time to calculate the central tendency, various measures of central tendency, our mean is often the best measure of central tendency, median is the center of a data set. It is best used when there are no extreme values in a data set mode is also a measure of central tendency, but rarely used. Similarly, various measures of spread our variation are.

So, standard deviation and variance are the most commonly used measures of spread. standard deviation is nothing but the square root of variance. range is also a measure of spread Often used. Now, let us carry out descriptive statistics with an example. prom scores of 35 students in a class to score are in front of you what information can we derive by seeing this data? As such, we cannot derive any information we need to use descriptive statistic technique to describe this data set.

One way of describing this data set is by classifying this data into groups. Either you can group into different classes like say scores between 30 to 35 etc. I have classified here with the score itself and checked, how many students have scored this particular marks we can see that one student scored 30 marks to student scored 35 marks. Similarly, six students scored 60 marks, those students scored 85 marks etc. This is nothing but the frequencies of data and the table is known as frequency distribution table. If we add the frequencies with each other we get the cumulative frequency Then it becomes cumulative frequency table.

Let us plot this graphically with marks at x axis and numbers of student scored their marks all the frequency at y axis. Now, plot the graph in the similar way we had plotted the shooter performance we get a shape similar to a bell the arrow shows the central tendency and how far the data are clustered around the central tendency is known as the spread of that data set. In other words, the variation in a set of data statistically, central tendency and variation is calculated as mean and standard deviation. mean is nothing, but the simple average of a set of data. sample mean is denoted as x bar, which calculated as, total of values divided by, number of data sets. Similarly, variance is denoted as s square.

The variation is calculated as either variance or standard deviation? variance is denoted as s square which is equal to total of x minus x bar divided by n minus one. Once we find out variance, standard deviation is just the square root of variance standard deviation s is equal to square root of sigma x minus x bar divided by n minus one. It is simple calculation when data set is small. Let us do it with the IQ scores of five students, the scores are 96 104 126 134 and 140. In order to calculate the mean, add all the individual values of x, which comes to 600.

Now divided with the number of observation batters 600 divided by five equals to 120. So the mean IQ score of five students is equal to 120. That means, x bar equals to 120 for calculating variation substract Each individual score from the mean score that is x minus x bar. Now, square these values and add together to get the total value as 1464. The calculation for variance is summation of x minus x bar old square divided by n minus one. This comes as 1464 divided by four equals to 366. standard deviation is just the square root of variance that is equal to Quiet Rudolph 366 equals to 19.13 manual calculation is easy when we deal with small set of data.

However, for large set we need to use Excel sheets or software that is find out mean and standard deviation in Minitab. I assume that you have already installed Minitab trial version. This is a practice session those who would like to practice download the file to dot mean at STD d eV from the link Double click on two dots mean and STD d v while calculating mean and standard deviation in Minitab. Click calc menu, column statistics. And the column statistics dialog box will open click mean or standard deviation, or median, etc. Whatever you need to find out, click on input variable and type supplier a or double click on supplier a on left tab, click OK to view the result on session window In this session window, we can see the result mean of the supplier a is equals to 40 repeat the exercise yourself for other suppliers to find out both mean and standard deviation this lecture and here we can proceed to the next lecture on data collection methods.

Thank you