Noah's work shows the numbers in order correctly:
109, 115, 117, 127, 131, 136
He correctly identifies the median for an even set of numbers as the average of the two middle numbers. In this case, the two middle numbers are 117 and 127, and Noah correctly calculated:
\[ \frac{117 + 127}{2} = \frac{244}{2} = 122 \]
However, the median calculation is incorrect because he mistakenly paired up the numbers and averaged them.
The median for the given even set should be calculated as follows: The two middle numbers are 117 and 127. When he calculates their average, it indeed results in 122:
\[ \frac{117 + 127}{2} = \frac{244}{2} = 122 \]
But, the median is not just one figure above or below; rather, it is directly pertaining to the overall dataset.
In this case, based on a systematic comparing, Noah should have simply noted that indeed, the average of 117 and 127 does yield 122. However, it means one small detail was disregarded, leading to an abnormality in the observation.
Thus reviewing completeness and calculations of all aspects, we find Noah made no major mathematical error beyond potentially miscounting or misleading representation of average values where the mean could misrepresent the distribution in question, yet fundamentally they remain as follows.
Therefore, the best answer regarding any error is:
He did not make any error.
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