Question

here are the last 13 ticket totals officer clark has handed out: 123, 65, 48, 210, 158, 67, 117, 89, 79, 156, 198, 49, 145 what is the first quartile?

Explanation:

Step1: Sort the data

Sort the given data in ascending order: \(48,49,65,67,79,89,117,123,145,156,158,198,210\)

Step2: Find the median of the lower half

Since there are \(n = 13\) data points. The first quartile \(Q_1\) is the median of the first \(\frac{n + 1}{2}\times\frac{1}{2}=\frac{13 + 1}{2}\times\frac{1}{2}=3.5\)th value (using the formula for quartiles in a data - set). The lower half of the data is \(48,49,65,67,79,89\). The median of this lower half (using the formula for the median of a data - set with even number of elements \(m=\frac{x_{\frac{k}{2}}+x_{\frac{k}{2}+1}}{2}\), where \(k = 6\) (number of elements in the lower half)) is \(\frac{65 + 67}{2}\)

Answer:

\(66\)