Question

for the data set shown, find the median, the 1st quartile, and the 3rd quartile. drag the correct values into the table. 7 8 11 13 15 16 19 20 24 25 27 27 29 30 31 32 13 22 28 20 14 29 minimum first quartile median third quartile maximum 7 32

Explanation:

Step1: Count the number of data points

There are \(16\) data points.

Step2: Find the median

The median is the average of the \(8^{th}\) and \(9^{th}\) data points. The \(8^{th}\) data point is \(20\) and the \(9^{th}\) data point is \(24\). So, the median is \(\frac{20 + 24}{2}=22\).

Step3: Find the first quartile (\(Q_1\))

The first quartile is the median of the lower half of the data. The lower half has \(8\) data points. The median of the lower half (the \(4^{th}\) and \(5^{th}\) data points) is \(\frac{13+15}{2} = 14\).

Step4: Find the third quartile (\(Q_3\))

The third quartile is the median of the upper half of the data. The upper half has \(8\) data points. The median of the upper half (the \(12^{th}\) and \(13^{th}\) data points) is \(\frac{27+29}{2}=28\).

Answer:

First quartile: \(14\), Median: \(22\), Third quartile: \(28\)