Question

what is the third quartile for the scores of 90, 85, 100, 50, 45, 70, 60, and 40? 60 87.5 90 80

Explanation:

Step1: Sort the data

First, sort the scores in ascending order: \(40,45,50,60,70,80,85,90,100\).

Step2: Find the position of the third - quartile

The formula for the position of the \(k\) - th quartile (\(Q_k\)) is \(i=\frac{k(n + 1)}{4}\), where \(n\) is the number of data points. For the third quartile (\(k = 3\)) and \(n=9\), we have \(i=\frac{3\times(9 + 1)}{4}=\frac{3\times10}{4}=7.5\).

Step3: Calculate the third - quartile

When \(i\) is not an integer, we use the formula \(Q_k=x_{j}+(i - j)(x_{j + 1}-x_{j})\), where \(j\) is the integer part of \(i\). Here, \(j = 7\) and \(i=7.5\), \(x_{7}=85\), \(x_{8}=90\). Then \(Q_3=85+(7.5 - 7)\times(90 - 85)=85 + 0.5\times5=87.5\).

Answer:

B. \(87.5\)