3 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 15 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 For an odd data set. odd number of data values, as we have here, the median is the middle data value of the ordered The median of the ordered data set 7 10 10 11 12 12 13 14 15 is 12 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. Consider the ordered list of data values. The median, Q, which was determined in the last step, has been underlined for clarity. 7, 10, 10, 11, 12, 12, 13, 14, 15 There are nine values in the whole data set, but there are only Xvalues to the left of the underlined median. The first quartile, Q, will be equal to the median of these values. 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. median = 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 Q1 = 2