Question

finally, find $q_3$. recall that the third quartile $q_3$ is the median of the upper half of the data. that is, the median of the data located above the $q_2$ position. consider the ordered list of data values. the location of the median ($q_2$), which was determined in the last step, is indicated for clarity. 11, 14, 16, 17, 17, 20, 21, 23, 29, 32, $q_2$, 32, 34, 35, 36, 37, 38, 40, 45, 45, 51. there are twenty values in the whole data set, but there are only values to the right of the median. the third quartile $q_3$ will be equal to the median of these values. since the upper 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 = $\frac{sum\\ of\\ middle\\ two\\ values}{2}$. the middle two values of the upper half of the data set are 37 and. now, calculate the third quartile, $q_3$. $q_3=\frac{37 + }{2}$

Explanation:

Step1: Determine number of values in upper - half

There are 20 values in total. The median divides the data into two halves. So, there are 10 values to the right of the median.

Step2: Identify middle two values of upper - half

The ordered upper - half data is 32, 34, 35, 36, 37, 38, 40, 45, 45, 51. The middle two values are 37 and 38.

Step3: Calculate the third quartile

Using the formula for median of even - numbered data set, $Q_3=\frac{37 + 38}{2}=\frac{75}{2}=37.5$

Answer:

37.5