 Hello and welcome to the session. In this session we will discuss measures of central tendency. To make out some important features of the data by considering only certain representatives of the data we use measures of central tendency or averages. There are three measures of central tendency for ungrouped data. The first one that we have is mean or we can also say average. Now the mean of the number of observations, the sum of the values of all the observations divided by the total number of observations. Mean is denoted by x bar and this is equal to summation xi i goes from 1 to n total upon n where we have these xi are the observations and n is the total number of observations. Now for ungrouped frequency distribution x bar is equal to summation fi xi i goes from 1 to n upon summation fi i goes from 1 to n. Here again xi are the observations and fi are the frequencies. The other measure of central tendency is the median. Basically median is the value of the middlemost observation or observations. Now if we have the total number of observations that is n is odd then the median in this case is the value of n plus 1 upon 2th observation and if we have the total number of observations that is n is even then the median is the mean of n upon 2th and n upon 2 plus 1th observations. Now the next measure of central tendency is mode. Mode is basically the most frequently occurring observation that is we can also say that it is an observation with the maximum frequency. Let's consider ungrouped data 1 2 5 3 4 6 0 5. Now first we will arrange this data in an ascending order or a descending order. Let's arrange it in an ascending order so we have 1 2 3 4 5 5 6. Now from this given data we have that the total number of observations that is n is equal to 8. Now the mean that is x bar is equal to the sum of the observations which is equal to 26 upon the total number of observations that is n. This is equal to 3.25. So mean for this data is 3.25. Now next let's find out the median. Now as you can see the total number of observations that is n is 8 which is even so median is given by the mean of the values of n upon 2 observation that is 8 upon 2 or you can say the 4th observation n upon 2 plus 1 observation that is 5th observation. Now from this data we have the 4th observation is 3 plus 5th observation is 4 upon 2. Now this is equal to 7 upon 2 which is equal to 3.5. So 3.5 is the median for the given data. Now mode as we know mode is the observation with the maximum frequency. So from this data we have that 5 is occurring two times that is it has the maximum frequency so mode is 5. So this is how we can find out mean, median and mode for an ungrouped data. This completes this session. Hope you have understood the measures of central tendency.