 Hello and welcome to the session. In this session we will discuss quartiles at interquartile range. Now we know that medium device a given series arranged in ascending or descending order into two equal parts. Now here we have to discuss quartiles. Now quartile is an important concept of statistics and quartiles are the values which split the arranged data that is an arranged data set into four identical pieces or we can say the quartiles divide the given series into four equal parts and for any series there are two quartiles denoted by Q1, Q2, Q3 or we can say there are three points of division which are Q1, Q2 and Q3. Now let us discuss this diagrammatically. Now for a given arranged data esm is called the median of the given data as it divides the given data into two equal parts that is em which is equal to Ms. Now again for this arranged data let us take three points Q1, Q2 and Q3. Now you can see that these three points divides or you can say that these three points are splitting the arranged data into four identical pieces that is these four identical pieces. Now here Q1 is called the lower quartile, Q2 is called the middle quartile, Q3 is called the upper quartile. Now the lower quartile cuts off the lower 25 percent of the data then the middle quartile cuts off the data partially that is 50 percent of the data and then the upper quartile the lower 75 percent of the data and the upper most 25 percent of the data. So this is the concept of quartiles where we are getting a lower quartile, a middle quartile which is also called the second quartile and as it divides the given data partially so this is called the medium of the given data and Q3 is the upper quartile. Now let us discuss the interquartile range now the difference between the upper and the low quartile values that is these values is called the interquartile range. So we have the interquartile range is equal to Q3 minus Q1. Now for getting quartiles the given series must be arranged in ascending order then the lower quartile Q1 is equal to n plus 1 by fourth term and the upper quartile Q3 is equal to 3 into n plus 1 the whole by fourth term also 50 percent of the distribution falls between the lower and the upper quartiles that is between Q1 and Q3. Now this is a very common effect that the large majority of items cluster generally closely to the average and the median and interquartile range provide us with measures of central tendency and dispersion respectively. Now the interquartile range is the difference between the lower and upper quartile values therefore it is immune from the disturbances caused by the incidence of extreme values and also it tells us the range of variability which is sufficient to contain 50 percent of the distribution. Now based on these formulas let us discuss an example now in this compute Q1 Q3 that is the lower and upper quartile and the interquartile range from the following series and that is 8 10 15 7 12 11 17 20 22. Now for the solution we have to arrange the given data in the ascending order in ascending order it will be 7 8 10 11 12 15 17 20 and 22 now the number of terms here is 9 now using this formula we can find out the lower quartile and using this formula we can find out the upper quartile so the lower quartile Q1 is equal to the value of n plus 1 whole upon 4 term which is equal to the value of now n is 9 and 9 plus 1 whole upon 4 is 10 by 4 and 10 by 4 is 2.5 so it is the value of 2.5 term which is equal to the value of second term plus 0.5 into value of third term minus value of second term the whole now here the second term in the given series is 8 and the third term is 10 so this is equal to 8 plus 0.5 into 10 minus 8 the whole which is equal to 8 plus now 0.5 into 2 is 1 so 8 plus 1 is equal to 9 therefore the value of the lower quartile is equal to 9 now the upper quartile Q3 is equal to the value of 3 into n plus 1 whole upon 4 term now n is 9 here so here it will be 9 plus 1 by 4 which is 10 by 4 which is equal to 2.5 so this is equal to value of 3 into 2.5 term which is equal to value of 7.5 term now this is equal to the value of the seventh term plus 0.5 into value of the eighth term minus value of the seventh term the whole now in the given series the seventh term is 17 and the eighth term is 20 so this is equal to 17 plus 0.5 into 20 minus 17 the whole which is equal to 17 plus 0.5 into 3 is 1.5 so this is equal to 18.5 now by using this formula we can find out the interquartile range now the interquartile range is equal to Q3 minus Q1 now this is the value of the lower quartile that is Q1 and this is the value of the upper quartile that is Q3 so this is equal to 18.5 minus 9 which is equal to 9.5 so in this way we have got the lower quartile the upper quartile and the interquartile range so in this session you have learnt about quartiles and interquartile range so this concludes our session hope you all have enjoyed this session