What is the five-number summary for this set of ages?

Question

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

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Answer 1

To calculate the five-number summary for the provided set of ages, we will follow these steps:

1. Sort the data: First, we need to sort the ages in ascending order.

   • Ages: 27, 27, 33, 36, 39, 40, 42, 46, 55

2. Identify the five-number summary:

   • Minimum: The smallest value in the dataset.
   • Q1 (First Quartile): The median of the first half of the data (the lower 25%).
   • Median: The middle value of the dataset.
   • Q3 (Third Quartile): The median of the second half of the data (the upper 25%).
   • Maximum: The largest value in the dataset.

Calculations:

1. Minimum:

   • The minimum is the first value in the sorted dataset: 27

2. Median:

   • The median is the middle value. Since there are 9 values (an odd number), the median will be the 5th value in the sorted list:
   • Median = 39

3. Q1:

   • Q1 is the median of the first half of the data: 27, 27, 33, 36 (the first four values). The median of these four values will be the average of the 2nd and 3rd values:
   • Q1 = (27 + 33) / 2 = 30

4. Q3:

   • Q3 is the median of the second half of the data: 40, 42, 46, 55 (the last four values). Again, we take the average of the 2nd and 3rd values:
   • Q3 = (42 + 46) / 2 = 44

5. Maximum:

   • The maximum value is the last value in the sorted dataset: 55

Summary:

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

Putting it all together, the five-number summary is:

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