First find the low and high numbers of the five number summary for the given data set Recall that the five number summary is used to create a box and whisker plot The five number summary consists of the lowest value the first quartile Q the median the third quartile Q3 and the highest value of a data set The given data set 7 10 10 11 12 12 13 14 15 is ordered We see that the lowest value is 7 7 and the highest value is 15 3 Step 2 Now find the median Recall that the median is the central value of an ordered distribution Note that the median is also the second quartile Q odd number of data values as we have here the median is the middle data value of the ordered For an odd data set The median of the ordered data set 7 10 10 11 12 12 13 14 15 is 12 Step 3 Next find Q Recall that the first quartile Q is the median of the lower half of the data That is the median of the data located below the Q position 7 10 10 11 12 12 13 14 15 There are nine values in the whole data set but there are only median The first quartile Q will be equal to the median of these values 15 Consider the ordered list of data values The median Q which was determined in the last step has been underlined for clarity sum of middle two values 2 The middle two values of the lower half of the data set are 10 and Now calculate the first quartile Q 10 10 2 median 12 2 Since the lower half of the data has an even number of data values we will now use the rule to find the median of an even number of data values x values to the left of the underlined