Question

204, 216, 111, 224, 230, 211, 210, 198, 200, 218
what numbers represent the range, lower quartile, and upper quartiles?
○ range: 210.5
lower quartile: 200
upper quartile: 218
○ range: 14
lower quartile: 111
upper quartile: 198
○ range: 119
lower quartile: 218
upper quartile: 200
○ range: 119
lower quartile: 200
upper quartile: 218

Explanation:

Step1: Sort the data

First, sort the data set \(204, 216, 111, 224, 230, 211, 210, 198, 200, 218\) in ascending order: \(111, 198, 200, 204, 210, 211, 216, 218, 224, 230\)

Step2: Calculate the range

The range is calculated as \( \text{Range}=\text{Max}-\text{Min}\). Here, \(\text{Max} = 230\) and \(\text{Min}=111\). So, \( \text{Range}=230 - 111=119\)

Step3: Calculate the lower quartile

The lower quartile (\(Q_1\)) is the median of the lower half of the data. The lower half of the data \(111, 198, 200, 204, 210\). The median of this set (since \(n = 5\), the middle - value is the third value) is \(200\)

Step4: Calculate the upper quartile

The upper quartile (\(Q_3\)) is the median of the upper half of the data. The upper half of the data \(211, 216, 218, 224, 230\). The median of this set (since \(n = 5\), the middle - value is the third value) is \(218\)

Answer:

range: \(119\), lower quartile: \(200\), upper quartile: \(218\) (the fourth option)