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2. The ages of the last 16 United States presidents on their first inauguration day are shown in the table below.

\begin{tabular}{|l|l|l|l|}
\hline
51 & 54 & 51 & 60 \\
\hline
62 & 43 & 55 & 56 \\
\hline
61 & 52 & 69 & 64 \\
\hline
46 & 54 & 47 & 70 \\
\hline
\end{tabular}

Determine the minimum, maximum, and interquartile range of the data set. You MUST state all three to receive full credit. Circle each of your answers.

(3 points)



Answer :

GinnyAnswer
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]

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