welcome to a lesson on quartiles and percentiles percentiles are used in statistics to indicate a value at or below which a certain percent of data values fall for example quartile 1 is the 25th percentile because 25 of the data values are at or below q1 this also means that 75 of the data values are at or above the 25th percentile looking at the graph above q1 is the 25th percentile because 25 of the data values these data values here are at or below q1 which also means that 75 of the data values these data values here are at or above the 25th percentile the median or q2 is the 50th percentile because 50 of the data values are at or below the median this also means that 50 percent of the data values are at or above the 50th percentile so looking back at the graph again the median is the 50th percentile because 50 of the data values these data values here are at or below the median which also indicates that 50 of the data values these values here are at or above the 50th quartile and then quartile 3 or q3 is the 75th percentile because 75 percent of the data values are at or below q3 which also means 25 percent of the data values are at or above the 75th percentile going back to the graph one last time q3 is the 75th percentile because 75 percent of the data values these data values here are at or below q3 which also indicates 25 of the data values these data values here are at or above the 75th percentile now let's look at some questions not involving the quartiles the first two statements involve the 28th percentile looking at the graph above the 28th percentile would be the data value approximately here where 28 of the data values these data values here are at or below the 28th percentile which also means that 100 minus 28 or 72 of the data values are at or above the 28th percentile so the first question is what percent of data values in a data set lie at or below the 28th percentile which would be 28 percent and the second question is what percent of data values in a data set lie at or above the 28th percentile which is 72 percent the next two questions involve the 70th percentile so going back to the graph the 70th percentile would be the data value approximately here where 70 of the data values these data values here are at or below the 70th percentile which means 30 of the data values are at or above the 70th percentile so reading carefully we're asked to find the percent of data values in a data set that lie at or above the 70th percentile which are these data values here which is 30 and now we're asked to find the percent of data values in a data set that lie at or below the 70th percentile which is 70 percent next if a sample consists of 800 test scores how many of them would be at or below the 32nd percentile the 32nd percentile is approximately here where 32 of the data values these data values here are at or below the 32nd percentile which means 68 of the data values are at or above the 32nd percentile so if the sample consists of 800 tests how many of them would be at or below the 32nd percentile that would be 32 percent of 800. which is equal to 0.32 times 800 which is 256. so if the sample consists of 800 test scores 256 of them would be at or below the 32nd percentile and for the last question if a sample consists of 800 tests how many of the tests would be at or above the 56 percentile the 56th percentile would be approximately here where 56 of the data values these data values here are added below the 56th percentile which means 44 percent of the data values are at or above the 56th percentile and the question is asking how many test scores would be at or above the 56th percentile which is going to be 44 of the 800 tests so 44 of 800 is equal to 0.44 times 800 which is 352. if a sample consists of 800 test scores 352 of them would be at or above the 56th percentile i hope you found this helpful