Consider the following ordered data.3   6   6   7   8   8   9   10   11(a) Find the low, Q1, median, Q3, and high.(b) Find the interquartile range.(c) Make a box-and-whisker plot.Step 1(a) Find the low, Q1, median, Q3, and high.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, Q1, the median, the third quartile, Q3, and the highest value of a data set.The given data set 3   6   6   7   8   8   9   10   11 is ordered.We see that the lowest value is and the highest value is .

The lowest value in the data set is 3 and the highest value is 11.

Next, we find the median (the middle number). If the data set has an odd number of observations, the median is the middle number. If the data set has an even number of observations, the median is the average of the two middle numbers. In this case, we have 9 observations, so the median is the 5th number, which is 8.

To find Q1 (the first quartile), we look at the lower half of the data (not including the median if the number of observations is odd). The lower half of the data is 3, 6, 6, 7, 8. The median of this lower half is 6, so Q1 is 6.

To find Q3 (the third quartile), we look at the upper half of the data (not including the median if the number of observations is odd). The upper half of the data is 8, 9, 10, 11. The median of this upper half is 9.5, so Q3 is 9.5.

Step 1(b) Find the interquartile range. The interquartile range (IQR) is Q3 - Q1. So in this case, IQR = 9.5 - 6 = 3.5.

Step 1(c) Make a box-and-whisker plot. To make a box-and-whisker plot, we draw a number line and mark the values of the five-number summary on it. We draw a box from Q1 to Q3 and draw a line at the median. Then we draw lines (the whiskers) from Q1 to the lowest value and from Q3 to the highest value.