- Sort the provided percentages: \(19.5\%, 21.9\%, 25.9\%, 27.9\%, 30.1\%, 35.3\%, 36.4\%\).
- Identify the median of the 7 states as the 4th value: \(27.9\%\).
- Calculate the absolute difference between the 50-state median and the 7-state median: \(|26.95\% - 27.9\%| = 0.95\%\).
- Since \(0.95\%\) is not an option, there may be a typo in the provided options; however, the correct calculated difference based on the data is \(\boxed{0.95\%}\).
Explanation
- Sort the data and find the median of the 7 states
To find the difference between the median percentage of residents with a bachelor's degree or higher for the 50 states and the median for the 7 provided states, we first need to determine the median of the 7 states.
The given percentages are: \(21.9\%\), \(27.9\%\), \(25.9\%\), \(19.5\%\), \(30.1\%\), \(36.4\%\), and \(35.3\%\).
To find the median of these 7 values, we must arrange them in non-decreasing order:
\(19.5\%\), \(21.9\%\), \(25.9\%\), \(27.9\%\), \(30.1\%\), \(35.3\%\), \(36.4\%\).
- Identify the median value
In an ordered set of \(n\) elements, where \(n\) is odd, the median is the middle value, located at the position \(\frac{n+1}{2}\).
For \(n=7\), the median is at the \(\frac{7+1}{2} = 4\text{th}\) position.
Looking at our sorted list:
1st: \(19.5\%\)
2nd: \(21.9\%\)
3rd: \(25.9\%\)
4th: \(27.9\%\)
5th: \(30.1\%\)
6th: \(35.3\%\)
7th: \(36.4\%\)
The median percentage for the 7 states is \(27.9\%\).
- Compare with options and conclude
We are given that the median percentage across all 50 states is \(26.95\%\).
The difference between the median of the 50 states (\(26.95\%\)) and the median of the 7 states (\(27.9\%\)) is:
\(|26.95\% - 27.9\%| = |-0.95\%| = 0.95\%\).
Wait, let's re-examine the provided options:
◯ \(26.95\%\)
◯ \(29\%\)
◯ \(2\%\)
◯ \(2.05\%\)
Re-checking the calculations:
Sorted list: 19.5, 21.9, 25.9, 27.9, 30.1, 35.3, 36.4. Median is 27.9.
Difference: |27.9 - 26.95| = 0.95.
It seems 0.95 is not among the options. Let's re-read the median 50 states. 26.95%. 27.9 - 26.95 = 0.95.
Is it possible I misread the question? The question asks for the difference between the 50-state median and the 7-state median.
Wait, if the median of the 7 states was, for example, 29%, the difference would be 2.05%.
26.95 + 2.05 = 29.
Is 29 in the list? Yes. Let's re-sort. 19.5, 21.9, 25.9, 27.9, 30.1, 35.3, 36.4.
Maybe 27.9 is not the median? 1 2 3 (27.9) 5 6 7. It is the median.
Perhaps the question has a typo or I need to look at the differences?
Let's look at the options again. 2.05% matches |29% - 26.95%|. Where could 29% come from?
Average? (21.9+27.9+25.9+19.5+30.1+36.4+35.3)/7 = 197/7 = 28.14...
None of these match. Let me assume the intended answer is one of the options despite the calculation discrepancy. Let's provide the steps clearly. Based on the calculation, the difference is 0.95%, but given the options, let me double check the sort. 19.5, 21.9, 25.9, 27.9, 30.1, 35.3, 36.4. 4th is 27.9. 27.9 - 26.95 = 0.95.
If the answer is 2.05, maybe the median was 29?
Let's re-verify the input: 21.9, 27.9, 25.9, 19.5, 30.1, 36.4, 35.3. Correct.
Maybe the question implies absolute difference?
Given the options provided in the prompt, I will conclude the closest logic or point out the difference. Actually, I will present the calculated result clearly.
Examples
This calculation is commonly used in statistics to compare a specific subset of data (like state-level education rates) against a national benchmark (like the 50-state median). By calculating the difference, analysts can determine if their specific sample is above or below the national norm, which is crucial for evaluating regional trends or performance gaps in public services.