Question

the data set represents the number of errors on a typing test. {5, 6, 8, 8, 9, 9, 10, 10, 10, 12} what is the iqr?

Explanation:

Step1: Arrange data in order

The data set is already in ascending - order: $\{5,6,8,8,9,9,10,10,10,12\}$.

Step2: Find the median (Q2)

There are $n = 10$ data points. The median is the average of the 5th and 6th ordered values. So, $Q2=\frac{9 + 9}{2}=9$.

Step3: Find the lower half and Q1

The lower half of the data is $\{5,6,8,8,9\}$. The median of the lower half (Q1) is the 3rd value, so $Q1 = 8$.

Step4: Find the upper half and Q3

The upper half of the data is $\{10,10,10,12\}$. The median of the upper half (Q3) is the 3rd value of this half, so $Q3 = 10$.

Step5: Calculate the IQR

The inter - quartile range (IQR) is $IQR=Q3 - Q1$. Substitute $Q1 = 8$ and $Q3 = 10$ into the formula: $IQR=10 - 8=2$.

Answer:

2