 Hello and welcome to the session. In this session we shall discuss how to choose the measure of center and variability for the given data. We have studied three measures of center that is mean, medium and mode. But the question arises for the given data which method should we use to find its center that is mean, medium or mode. The choice of measure of center depends on three main things. First, extreme values of the outliers. Second, data set having many identical numbers. And third, gaps in the middle of data. Let us consider the three data sets. Now in the first data set we see that there are seven items having value 5. Let us make a dot plot for this data. In this data one is given once so we mark one once. Two is given two times so we mark two twice. Three is given once so we mark three once. Four is given twice so we mark four twice. Five is given seven times so we mark five seven times. And six is given twice so we mark six two times. Now clearly we can see that five is mode as it has the highest frequency. So in this case mode is the appropriate choice of center. Now we take the second set of data which is given as two three five six seven one eight six. Now we see that there are no outliers here so we can find mean. We can also choose median but mean is a more appropriate choice than median because it will take into consideration all the data values rather than only the middle value. So we find mean and we know that mean is given by some of all the values divided by the total number of terms in the data set. So we have two plus three plus five plus six plus four plus seven plus one plus eight plus six divided by nine. And the sum is equal to forty two and we divide it by nine and therefore we get four point six six at the moon and to find median. We erase this data set in the ascending order. Now we know that median is given by the middle most term in the series. And there are all number of terms given. So the fifth term is the middle most term. Therefore the median is given by five which is the fifth term in the series. Whenever we can use both mean and median we see that there is not much difference between the values of mean and median. Now we take another data set that is two five sixty three six five three and two. And here we notice that there are no big gaps and there exists an outlier sixty that is the value which is very large from rest of the values. That is we have an outlier and its value is given as sixty. Since there is an outlier so we suppose to choose mean as the measure of center and mean is given by some of all the values divided by the total number of terms in the series. And here we have the sum as two plus five plus sixty plus three plus six plus four plus three plus two divided by eight. Which is equal to eighty five by eight that is ten point six so we get the value of mean as ten point six. And if we choose median as the measure of center to find median we first arrange the series in ascending order. Now we know that median is the median value and since there are even number of terms in the series that is we have eight terms. So median will be given by the mean of maybe two terms that is the fourth term and the fifth term. So median is given by mean of fourth and fifth term. The fourth term is given by three and the fifth term is given by four and mean of these two terms is given by three plus four by two which is equal to seven upon two that is three point five. So for this series we get the value of mean as ten point six and the value of median is three point five. Now we see that all values except sixty are near to median but no value is near to mean. So we say mean is affected by extreme value because it is sum of all the values divided by the number of terms in data and here among all values we add a very large value to all other values which will have effect on the calculation. So it is appropriate to use median when outlier is given the gap between the values is not much and median a positional average it is not affected by outliers. Now we can summarize the above explanation as when there are no outliers given then mean is useful and median is useful when there are outliers or extreme values and no big gap between values of data and mode is useful when the data has many identical numbers. Now we are going to discuss choice of measure of variation that is how to choose the measure of variation for the given data. We have divided three measures of variation that is range, interquartile range, mean absolute deviation. Now range only takes into consideration the minimum and the maximum values. It does not consider all the values so range is not always reliable. Whenever we have an outlier we always use center as median thus here the variation should be measured using interquartile range especially when we use box and whisker plot to represent the data when we choose mean as center. So it is appropriate to use mean absolute deviation to measure variation. It is complete file version. Hope you enjoyed this version.