 Hello and welcome to the session. In this session we are going to discuss other partition values for frequency distributions. As we know that mediums divide the given series of distribution into two equal parts. Likewise quartile divides the data into four equal parts. Quintile into type equal parts, sextile into six equal parts, decimal into ten equal parts and percentile into hundred equal parts. All these mentioned above are the points of division. Now we shall discuss three useful measures which divide the series into four, ten or hundred equal parts that is quartiles, decimal and percentiles. First we are going to discuss quartiles. As we have discussed quartiles divides a series into four equal parts and the number of points dividing the series is always one less than the number of subgroups. Therefore for any series there are three quartiles that is Q1, Q2 and Q3. Q1 is known as first or lower quartile covering 25% items. The second quartile Q2 is the same as the medium of the series or fifth decimal or the 58th percentile Q3 is the third or upper quartile covering 75% items and hence it is same as the 75th percentile. The difference between upper quartile and lower quartile is called interquartile range. Quartile deviation which is also known as semi interquartile range is given by Q3 minus Q1 whole upon two. Now we shall discuss formula for finding quartiles for individual and discrete series. Lower quartile Q1 is given by N plus 1 by fourth item where N is equal to summation of F for discrete series is equal to number of observations for individual series. For continuous series lower quartile Q1 is given by N plus I upon F into N by fourth minus C of N by fourth item is considered where L is the lower limit of the quartile plus I is the width of the class interval. F is the frequency of the quartile class C is the cumulative frequency of the class just lower than the quartile class and N is the sum of the frequencies given by summation of F. And similarly upper quartile Q3 is given by 3 into N plus 1 by fourth item where N is equal to summation of F that is the sum of the frequencies for discrete series is equal to number of observations for individual series. And for continuous series upper quartile Q3 is equal to L plus I upon F into 3 into N by 4 minus C five over 3 into N by fourth item is considered where L is the lower limit of the quartile class I is the width of the class interval. F is the frequency of the quartile class C is the cumulative frequency of the class just lower than the quartile class and N is equal to the sum of the frequencies given by summation of F. Now we are going to discuss decals. It divides a series into 10 equal parts. There are 9 decals for any series denoted by D1, D2, D3 up to Dn known as first decimal, second decimal and so on up to ninth decimal. The difference D9 minus D1 that is between the upper decimal and lower decimal is called inter decimal range here D1 is given by N plus 1 by tenth item. Similarly D7 is given by 7 into N plus 1 by tenth item and D9 is given by 9 into N plus 1 by tenth item where N is equal to summation of F for discrete series. N is equal to number of observations for individual series for continuous series D1 that is the first decimal is given by N plus I upon F into N by 10 minus of C where the size of N by tenth item is considered where L is equal to the lower limit of the decimal class I is the width of the class interval F is the frequency of the decimal class C is the cumulative frequency of the class just lower than the decimal class and N is the sum of the frequencies which is given by summation of F. Now we are going to discuss percentiles. It divides a given series into 100 equal parts. There are 99 percentiles for a given series denoted by P1, P2, P3 up to P99. The difference that is P90 minus P10 between the upper percentile and the lower percentile is called inter percentile range and P1 is given by N plus 1 by 100 item P47 is given by 47 into N plus 1 by 100th item where N is equal to the sum of the frequencies that is summation of F for discrete series and N is equal to number of observations for individual series for continuous series P1 is given by N plus I upon F into N by 100 minus C where N by 100th item is considered. Similarly P47 is given by N plus I upon F into 47 into N by 100 minus C P7 into N by 100th item is considered where L is equal to lower limit of the percentile class I is the width of the class interval F is the frequency of the percentile class C is the cumulative frequency of the class just lower than the percentile class and N is the sum of the frequencies given by summation of F. We should observe that for continuous series we use N by 10 for the 4th percentile, 2 into N by 10 for the 2nd percentile, 3 into N by 10 for the 3rd percentile and so on up to 9 into N by 10 for the 9th percentile and for percentile we use N by 100 for the 4th percentile, 2 into N by 100 for the 2nd percentile, 3 into N by 100 for the 3rd percentile. And in the case of individual and discrete series L is replaced by N plus I let us take an example calculate the quartiles interquartile range H decimal and P47 for the following data that is 4, 3, 1, 5, 7, 6, 2, 10, 8 and 9. We should first arrange the data in ascending order. Now we can first find out lower quartile Q1 which is given by the size of N plus 1 by first item here the value of N is equal to 10. Q1 is equal to 10 plus 1 that is 11 by 4th item 11 by 4 is equal to 2.75. Therefore Q1 is given by the size of 2.75 item which is equal to size of 2nd item plus 0.75 into size of 3rd item minus size of 2nd item. The second item is given by 2 and the third item is given by 3. So we have the size of 2nd item that is 2 plus 0.75 into size of 3rd item minus size of 2nd item that is 3 minus 2 which is equal to 1. Therefore we have 2 plus 0.75 which is equal to 2.75. Therefore lower quartile Q1 is equal to 2.75. Now we should find out upper quartile Q3 which is given by the size of 3 into N plus 1 by 1st item which is equal to size of 3 into N plus 1 by 4th and the value of N is equal to 10. So we have 3 into 11 by 4th item which is equal to 3 into 2.75 item and by 4 is equal to 2.75 which is equal to size of 3 into 2.75 that is 8.2 size item which is equal to size of 8th item plus 0.2 size into 2.75 item. Size of 9th item minus 8th item is the size of 8th item is equal to 8 and the size of 9th item is given by 9. So we have size of 8th item that is 8 plus 0.25 into size of 9th item that is 9 minus size of 8th item that is 8 which is equal to 9 minus 8 that is 1. So we have 8 plus 0.25 which is equal to 8.25. Therefore upper quartile Q3 is equal to 8.25. Now we know that interquartile range is given by upper quartile minus lower quartile that is Q3 minus Q1 and we know that Q3 is equal to 8.25 minus Q1 that is 2.75 is equal to 5.5. Therefore interquartile range is equal to 5.5. Now we are going to find out 8th decimal that is denoted by D8 is given by the size of 8 into n plus 1 by 10th item. And n is equal to 10 so we have the size of 8 into 10 plus 1 that is 11 by 10th item which is equal to size of 11 into 8 that is 8 to 8 by 10th item. Which is equal to size of 8.8 item that is we have size of 8 item plus 0.8 into size of 9th item minus 8th item. So we have the size of 8th item that is given by 8 plus 0.8 into size of 9th item minus size of 8th item that is size of 9th item is given by 9 minus size of 8th item which is given by 8. So we have 8 plus 0.8 into 9 minus 8 that is 1 which is equal to 0.8 which plus 0.8 is given by 8.8. Therefore we get the value of 8th decimal D8 as 8.8. Now we are going to find 47th percentile that is P47 is given by the size of 47 into n plus 1 by 100th item. Here the value of n is 10 so we have the size of 47 into 11 by 100th item which is equal to size of 517 by 100th item. That is equal to the size of 517th item that is the size of 5th item plus 0.17 into size of 6th item minus 6th item. Now the size of 5th item is given by 5 and the size of 6th item is given by 6. So we have the size of 5th item that is 5 plus 0.17 into size of 6th item that is 6 minus size of 5th item that is 5 which is equal to 5 plus 0.17 into 6 minus 5 that is 1 which is equal to 0.17 into 1 that is 0.17. And therefore we have 5 plus 0.17 which is equal to 5.17. Therefore P47 that is 47th percentile is given by 5.17. Thus we get the value of lower quartile Q1 as 2.75. The value of upper quartile Q3 as 8.25. The value of inter quartile range is given by 5.5. 8 decimal D8 is given by 8.8 and 47th percentile P47 is equal to 5.17. This completes our session. Hope you enjoyed this session.