The data set of prescription costs, in is displayed. 45 39 59 193 65 93 219 183 109 472 219 286 176. The first and third quartiles are Q_(1)=65 and Q_(3)=219 Q_(1)=126 and Q_(3)=345.5 Q_(1)=193 and Q_(3)=472 Q_(1)=62 and Q_(3)=219

To find the first and third quartiles of the given data set, we need to follow these steps:<br /><br />1. Arrange the data in ascending order.<br />2. Find the median (Q2).<br />3. Find the first quartile (Q1) and the third quartile (Q3).<br /><br />Given data set: $45, 39, 59, 193, 65, 93, 219, 183, 109, 472, 219, 286, 176$<br /><br />Step 1: Arrange the data in ascending order:<br />$39, 45, 59, 65, 93, 109, 176, 183, 193, 219, 219, 286, 472$<br /><br />Step 2: Find the median (Q2):<br />Since there are 13 data points, the median will be the 7th value.<br />Median (Q2) = 176<br /><br />Step 3: Find the first quartile (Q1) and the third quartile (Q3):<br />Q1 is the median of the lower half of the data (excluding the median).<br />Q1 = median of $39, 45, 59, 65, 93, 109, 176$<br />Q1 = 65<br /><br />Q3 is the median of the upper half of the data (excluding the median).<br />Q3 = median of $183, 193, 219, 219, 286, 472$<br />Q3 = 219<br /><br />Therefore, the correct answer is:<br />$Q_{1}=65$ and $Q_{3}=219$