What is the five-number summary for this set of ages? 40, 55, 27, 36, 33, 42, 46, 27, 39 (5 points) The minimum of the dataset is The value for Q1 is The median of the dataset is The value for Q3 is The maximum of the dataset is

Answer 1

To find the five-number summary for the set of ages \(40, 55, 27, 36, 33, 42, 46, 27, 39\), we first need to sort the data in ascending order:

1. Sort the dataset: \[ 27, 27, 33, 36, 39, 40, 42, 46, 55 \]

2. Identify the minimum and maximum:

   • Minimum: The smallest value in the set is \(27\).
   • Maximum: The largest value in the set is \(55\).

3. Find the median: The median is the middle value. Since there are 9 numbers (an odd count), the median is the 5th number in the sorted list:

   • Median: \(39\)

4. Find Q1 (the first quartile): Q1 is the median of the first half of the data (the numbers to the left of the median): \[ 27, 27, 33, 36 \] The median of this part (the average of 27 and 33) is: \[ Q1 = \frac{27 + 33}{2} = 30 \]

5. Find Q3 (the third quartile): Q3 is the median of the second half of the data (the numbers to the right of the median): \[ 40, 42, 46, 55 \] The median of this part (the average of 42 and 46) is: \[ Q3 = \frac{42 + 46}{2} = 44 \]

Now, we can summarize these findings:

• Minimum: \(27\)
• Q1: \(30\)
• Median: \(39\)
• Q3: \(44\)
• Maximum: \(55\)

Thus, the five-number summary for the dataset is:

• Minimum: \(27\)
• Q1: \(30\)
• Median: \(39\)
• Q3: \(44\)
• Maximum: \(55\)