Question

the purpose of this pretest is to assess your mastery of the standards covered in this module. you will be able to take this pretest exhibit mastery at a level of 60% or higher, you will be permitted to proceed to the next module without further review of this co if, however, you score below 60%, you will need to proceed through the items in this module to prepare for the module exam. question 5 what is the value of q3 for this dataset? {70, 89, 28, 67, 91, 19, 6} 70 67 19 89

Explanation:

Step1: Order the dataset

First, we order the dataset \(\{70, 89, 28, 67, 91, 19, 6\}\) from smallest to largest.
Sorting gives us: \(\{6, 19, 28, 67, 70, 89, 91\}\)

Step2: Find the median (Q2)

The number of data points \(n = 7\) (odd). The median (Q2) is the middle value, which is the \(\frac{n + 1}{2}=\frac{7+ 1}{2}=4^{\text{th}}\) value.
Looking at the ordered dataset, the \(4^{\text{th}}\) value is \(67\), so \(Q2 = 67\).

Step3: Find Q3

Q3 is the median of the upper half of the data. The upper half of the data (values greater than Q2) is \(\{70, 89, 91\}\).
The number of values in the upper half is \(3\) (odd). The median of this subset is the \(\frac{3+ 1}{2}=2^{\text{nd}}\) value.
Looking at \(\{70, 89, 91\}\), the \(2^{\text{nd}}\) value is \(89\). So, \(Q3 = 89\).

Answer:

89