 Quartiles and Percentiles

Quartiles  A quartile divides a sorted (least to greatest) data set into 4 equal parts, so that each part represents ¼ of the data set. Lower Quartile Q 1 Median M Upper Quartile Q 3

Quartiles  25% of all the data has a value less than or equal to Q 1  50% of all the data has a value less than or equal to M  75% of all the data has a value less than or equal to Q 3  50% of all the data lies between Q 1 and Q 3 Lower Quartile Q 1 Median M Upper Quartile Q 3

Quartiles  If a measurement falls to the right of the upper quartile of a set of data, then we know that it is in the top 25% of the data.  We also know that it is higher than at least 75% of the data  If a measurement falls to the left of the lower quartile of a set of data, then we know that it is in the bottom 25% of the data.  We also know that it is lower than at least 75% of the data. Lower Quartile Q 1 Median M Upper Quartile Q 3

Examples: 3, 4, 5, 6, 6, 7, 8, 9, 9, 10, 11  There are 11 data items  The median is the 6 th item. So M=7.  The lower quartile is the 3 rd item. (It is the middle of the lower half.) Q 1 =5  The upper quartile is the 9 th item. (It is the middle of the upper half.) Q 3 =9

What does this mean? 3, 4, 5, 6, 6, 7, 8, 9, 9, 10, 11  ¼ of 25% of the data has a value that is less than or equal to 5.  ½ or 50% of the data has a value that is less than or equal to 7.  ¾ or 75% of the data has a value that is less than or equal to 9.  ½ or 50% of the data lies between 5 and 9. Lower Quartile Q 1 Median M Upper Quartile Q 3

Percentiles  A percentile is a measure that tells us what percent of the total frequency is below that measure.  Percentiles Percentiles  The word percentile comes from the Latin words per centum which means “per hundred”.  Percentiles are generally used with large sets of data so that dividing it up into 100 equal parts seems realistic.

Percentiles  Suppose your grade in this class is at the 98 th percentile. Is this good or bad?  It means that you have a higher grade than 98% of the class.  Suppose your grade in this class is at the 3 rd percentile. Is this good or bad?  It means that you have a higher grade than 3% of the class.  Or, you can think of it this way: 97% of the class has a better grade than you 

 To find the percentile rank of a set of a score, x, out ofa set of n scores, where x is not included:

Example: Percentiles  70 th percentile for a test was 16/20. What does this mean?  70% got a 16/20 (80) or less.  30% got more than a 16/20 (80).