 Hello and welcome to the session. In this session we are going to discuss about mode. Mode can be defined as the value which occurs most often in a series. It can also be said that mode is that measure of observation around which items are most densely or heavily concentrated. Mode is that value which occurs most frequently but this does not imply that its frequency represents a majority out of all the total number of frequencies. For example, if out of 100 people, movie first is like the 32, movie second is like the 37 and movie third is like the 21, then it will be wrong to conclude that majority is with movie second, 21 plus 32 that is 53 have other preferences. Next we are going to discuss how to compute mode for different series. Let us consider the following distribution where the x values are given as 1, 2, 3 and 4 with the corresponding frequencies given by 5, 20, 10 and 3. Here 20 is the maximum frequency with the corresponding value of x as 2. Therefore, the mode of the given distribution is to let us take another example. Suppose 10 students are the following maximum mathematics that is 32, 60, 78, 35, 60, 90, 98, 90, 90 and 94. Here 90 has the maximum frequency that is 3. Therefore, the mode is 90 that in certain cases there may not exist a mode but there may be more than one mode. Thus in the first series that is 32, 60, 78, 45 and 90, there is no mode. In the second series that is 32, 60, 78, 45, 60, 90, 98 and 90, there are two modes that is 60 and 90. A series having one mode is called unimodal, a series having two modes is called diamodal, a series having three modes is called tri-modal and a series having more than three modes is called multimodal. Now we shall learn how to compute mode for individual series. There are two methods for computing mode for individual series and the first method is inspection method. In this method, we identify the value which occurs most frequently in a series. For example, we need to find the mode for the given series. Here by inspection, we can say that the mode of the series is 5 as it occurs most frequently. Second method is by converting individual series into discrete series. When the number of items in a series is very large, then we convert individual series into discrete series and then identify the value corresponding to which there is highest frequency We need to compute mode for this given series and since the number of items in this series is large, therefore first we convert the given series into discrete series. In the given distribution, 10 occurs 3 times, 11 occurs 6 times, 12 occurs 3 times, 13 occurs 3 times, 14 occurs 1s, 15 occurs 3 times, 16 occurs 3 times, 17 occurs 2 times, 18 occurs 3 times, 19 occurs 4 times and 20 occurs 1s. Now here, since the maximum frequency would be corresponding x value as 11, therefore the mode and value is 11. Now we can learn how to compute mode for discrete series. In a discrete series, mode can be determined by two methods and the first method of inspection. In inspection, the value which occurs most frequently identified as mode next is grouping method. There are cases when the value with maximum frequency may not be the modal value, that is when the difference between the maximum frequency, the frequency just lower or just higher is very less, that is the items are concentrated at more than one value, the immediate neighborhood of the highest frequency has very low frequency. In such cases, the grouping method is followed. Let us take an example, the time in the mode for the following distribution. Here in this distribution, the size is given as 28, 30, 32, 34, 36, 38 and 40, with the corresponding frequency represented by us as 3, 7, 8, 6, 2, 9 and 1. Now in this distribution, as the highest frequency is of 38, that is 9, the concentration appears to be greater around 8, therefore we should prepare a grouping and an analysis table. First we should prepare the grouping table and it consists of 6 columns and we write the given frequency in the first column. Now we group the frequencies in 2's and write their total in column 2, so we have 3 plus 7, that is 10, 8 plus 6, that is 14 and 2 plus 9, that is 11. Now leaving the first frequency, group the remaining frequencies in 2's and write their total in column 3. Therefore we have 7 plus 8, that is 15, 6 plus 2, that is 10 and leaving the last frequency 9. Now we group the frequencies in 3's and write their total in column 4, so we have 3 plus 7 plus 8, that is 18 and 6 plus 2 plus 9, that is 17. Leaving the first frequency, we group the remaining frequencies in 3's and write their total in column 5 and we have 7 plus 8 plus 6, that is 21 and leaving the last 2 frequencies. Leaving the first 2 frequencies, group the remaining frequencies in 3's and write their total in column 6, so we have 8 plus 6 plus 2, that is 16 and leaving the last frequency, that is 9. Now we mark the highest total in each column, in column 1, 9 is the highest total, in column 2, it's 14, in column 3, it's 15, in column 4, 18 is the highest total, in column 5, 21 is the highest total, in column 6, 16 is the highest total, this is the required grouping table and with the help of this table, we shall prepare an analysis table. In the analysis table, we write column number on the left side and the moving values of each column on the right side. Now in column 1, 9 is the maximum frequency whose corresponding x value is 38, therefore we mark the value of 38 in column 1. Now in column 2, 14 is the maximum frequency whose corresponding x values are 32 and 34, therefore we mark the value of 32 and 34 in column 2, in column 3, 15 is the maximum frequency whose corresponding x values are 30 and 32, therefore we mark the value of 30 and 32 in column 3, in column 4, 18 is the maximum frequency whose corresponding x values are 28, 30 and 32, therefore we mark the value of 28, 30 and 32 in column 4, in column 5, 21 is the maximum frequency whose corresponding x values are 30, 32 and 34, therefore we mark the value of 30, 32 and 34 in column 5 and 16 is the maximum frequency in column 6, whose corresponding x values are 32, 34 and 36, therefore we mark the value of 32, 34 and 36 in column 6. Now we write the total against each column, now the value which is repeated the maximum number of times will be the mode. Here 5 is the maximum total whose corresponding x value is 32, therefore the mode for this distribution is 32 and not 38, therefore the modal value is 32 with frequency 8, this completes our session, hope you enjoyed this session.