Question

for the data set shown, find the median, the 1st quartile, and the 3rd quartile. drag the correct values into the table. 16 24 12 41 30 35 minimum 4 first quartile drag and drop an item here median drag and drop an item here third quartile drag and drop an item here maximum 48

Explanation:

Step1: Count the number of data points

There are \(n = 20\) data points.

Step2: Find the median

For \(n = 20\) (even), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. \(\frac{n}{2}=10\), \(\frac{n}{2}+1 = 11\). The 10th value is \(21\) and the 11th value is \(27\). Median \(=\frac{21 + 27}{2}=24\).

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

The lower half of the data (first 10 values). For \(n_1=10\) (even), \(Q_1\) is the average of the 5th and 6th values of the lower - half. The lower - half data is \(4,5,8,9,11,13,17,17,20,21\). The 5th value is \(11\) and the 6th value is \(13\). \(Q_1=\frac{11+13}{2}=12\).

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

The upper half of the data (last 10 values). For \(n_2 = 10\) (even), \(Q_3\) is the average of the 5th and 6th values of the upper - half. The upper - half data is \(27,28,31,32,34,36,41,42,47,48\). The 5th value is \(34\) and the 6th value is \(36\). \(Q_3=\frac{34 + 36}{2}=35\).

Answer:

First quartile: \(12\), Median: \(24\), Third quartile: \(35\)