Question

find the median, first quartile (q1) and the third quartile (q3) for the data shown, which is already sorted. the number of data is n = 8. do not round your answers. x 18 20 21 23 23 25 28 29 median = q1 = q3 = > next question

Explanation:

Step1: Calculate median position

For \(n = 8\) (even - numbered data set), median position is \(\frac{n}{2}\) and \(\frac{n}{2}+ 1\). Median is the average of values at these positions. \(\frac{n}{2}=\frac{8}{2}=4\), \(\frac{n}{2}+1 = 5\). The 4th and 5th values are 23 and 23.
Median\(=\frac{23 + 23}{2}=23\)

Step2: Calculate Q1 position

The lower - half of the data for \(n = 8\) is the first 4 values. For the lower - half data set (\(n_1=4\), even - numbered), Q1 position is \(\frac{n_1}{2}\) and \(\frac{n_1}{2}+1\). \(\frac{n_1}{2}=\frac{4}{2}=2\), \(\frac{n_1}{2}+1 = 3\). The 2nd and 3rd values of the lower - half data set are 20 and 21. Q1\(=\frac{20 + 21}{2}=20.5\)

Step3: Calculate Q3 position

The upper - half of the data for \(n = 8\) is the last 4 values. For the upper - half data set (\(n_2 = 4\), even - numbered), Q3 position is \(\frac{n_2}{2}\) and \(\frac{n_2}{2}+1\). \(\frac{n_2}{2}=\frac{4}{2}=2\), \(\frac{n_2}{2}+1 = 3\). The 2nd and 3rd values of the upper - half data set are 25 and 28. Q3\(=\frac{25+28}{2}=26.5\)

Answer:

Median: 23
Q1: 20.5
Q3: 26.5