Question

The data below shows the hourly pay, in dollars, for all employees at a local business: 15, 24, 18, 15, 23, 28, 19, 22, 24, 27, 20, 16

Find the five-number summary.

Answer 1

The five-number summary includes the minimum, first quartile, median, third quartile, and maximum. For the given data, the summary is: Minimum = 15, Q1 = 18.5, Median = 21, Q3 = 24, Maximum = 28.

Step-by-step explanation:

The question you've posed pertains to finding the five-number summary of a given data set. The five-number summary consists of the minimum value, first quartile (Q1), median (Q2), third quartile (Q3), and maximum value. Here are the steps we'll take to find these statistics:

1. First, arrange the data in ascending order: 15, 15, 16, 18, 19, 20, 22, 23, 24, 24, 27, 28.
2. Determine the minimum value: 15.
3. Calculate Q1, the median of the lower half of the data (excluding the median if the number of data points is odd): Median of 15, 15, 16, 18, 19, 20 is (18+19)/2 = 18.5.
4. Find the median of the entire data set: Median of 15, 15, 16, 18, 19, 20, 22, 23, 24, 24, 27, 28 is (20+22)/2 = 21.
5. Calculate Q3, the median of the upper half of the data: Median of 22, 23, 24, 24, 27, 28 is (24+24)/2 = 24.
6. Determine the maximum value: 28.

Therefore, the five-number summary is: Minimum = 15, Q1 = 18.5, Median = 21, Q3 = 24, Maximum = 28.