Question

formula 0.5 points
for the following data set, what is the first quartile?
{{45,48,52,60,67,76,77,79,82,92}}
answer

Explanation:

Step1: Sort the data

The data set is already sorted: \(45, 48, 52, 60, 67, 76, 77, 79, 82, 92\)

Step2: Calculate the position of the first quartile

The formula for the position of the first quartile \(Q_1\) is \(i=\frac{n + 1}{4}\), where \(n\) is the number of data points. Here \(n = 10\), so \(i=\frac{10+ 1}{4}=2.75\)

Step3: Interpolate to find \(Q_1\)

The first quartile is \(Q_1=x_{2}+0.75\times(x_{3}-x_{2})\)
\(x_{2} = 48\), \(x_{3}=52\)
\(Q_1=48+0.75\times(52 - 48)\)
\(Q_1=48 + 0.75\times4\)
\(Q_1=48+3\)

Answer:

\(51\)