Question

163, 97, 184, 199, 169, 175
what numbers represent the lower and upper quartiles?
○ lower quartile: 163
upper quartile: 184
○ lower quartile: 163
upper quartile: 172
○ lower quartile: 172
upper quartile: 184
○ lower quartile: 184
upper quartile: 163

Explanation:

Step1: Sort the data set

First, sort the data set \(97, 163, 169, 175, 184, 199\).

Step2: Find the median

Since there are \(n = 6\) data points. The median is the average of the \(3^{rd}\) and \(4^{th}\) values. \(Median=\frac{169 + 175}{2}=172\).

Step3: Find the lower half and upper half

The lower - half data set is \(97, 163, 169\) and the upper - half data set is \(175, 184, 199\).

Step4: Find the lower quartile (\(Q_1\))

For the lower - half data set (with \(n = 3\) data points), the lower quartile \(Q_1\) is the \(2^{nd}\) value. So \(Q_1 = 163\).

Step5: Find the upper quartile (\(Q_3\))

For the upper - half data set (with \(n = 3\) data points), the upper quartile \(Q_3\) is the \(2^{nd}\) value. So \(Q_3=184\).

Answer:

lower quartile: 16[LLM SSE On Failure]