Given the following dataset, what is the

Question

first quartile? Round to the nearest
tenth if necessary.
42, 82, 67, 34, 54, 62, 17, 47, 56, 18,
20

Answer 1

To find the first quartile (Q1) of a dataset, you need to follow these steps:

1. Sort the dataset in ascending order: \[ 17, 18, 20, 34, 42, 47, 54, 56, 62, 67, 82 \]

2. Determine the position of the first quartile: The formula for finding the position of Q1 is: \[ Q1 = \frac{(n + 1)}{4} \] where \( n \) is the number of observations in the dataset. In this case, \( n = 11 \): \[ Q1 = \frac{(11 + 1)}{4} = \frac{12}{4} = 3 \] This means that Q1 is located at the 3rd position in the sorted dataset.

3. Identify the value at this position: From our sorted dataset: \[ 17, 18, \textbf{20}, 34, 42, 47, 54, 56, 62, 67, 82 \] The 3rd value is 20.

Thus, the first quartile (Q1) of the dataset is 20.