Let's begin by organizing and calculating the required statistics from the given dataset.
1. Minimum Age:
First, identify the smallest age in the dataset:
[tex]\[51, 54, 51, 60, 62, 43, 55, 56, 61, 52, 69, 64, 46, 54, 47, 70\][/tex]
Clearly, the minimum age is:
[tex]\[\boxed{43}\][/tex]
2. Maximum Age:
Next, identify the largest age in the dataset:
[tex]\[51, 54, 51, 60, 62, 43, 55, 56, 61, 52, 69, 64, 46, 54, 47, 70\][/tex]
Clearly, the maximum age is:
[tex]\[\boxed{70}\][/tex]
3. Interquartile Range (IQR):
To calculate the IQR, follow these steps:
- Step A: Sort the ages in ascending order:
[tex]\[43, 46, 47, 51, 51, 52, 54, 54, 55, 56, 60, 61, 62, 64, 69, 70\][/tex]
- Step B: Determine the first quartile (Q1) and the third quartile (Q3).
To find Q1 (the 25th percentile), locate the value that marks the first quarter of the dataset:
For a dataset with 16 values:
[tex]\[Q1 = \text{value at the 4.25th position}\][/tex]
Interpolate as necessary to find:
[tex]\[Q1 = 51.0\][/tex]
To find Q3 (the 75th percentile), locate the value that marks the third quarter of the dataset:
[tex]\[Q3 = \text{value at the 12.75th position}\][/tex]
Interpolate as necessary to find:
[tex]\[Q3 = 61.25\][/tex]
- Step C: Calculate the IQR by subtracting Q1 from Q3:
[tex]\[
\text{IQR} = Q3 - Q1 = 61.25 - 51.0 = 10.25
\][/tex]
So, the Interquartile Range (IQR) is:
[tex]\[\boxed{10.25}\][/tex]
In summary:
- Minimum age: [tex]\(\boxed{43}\)[/tex]
- Maximum age: [tex]\(\boxed{70}\)[/tex]
- Interquartile Range (IQR): [tex]\(\boxed{10.25}\)[/tex]
