To determine how the mean would change if one of the 26's in the set \( { 26, 40, 47, 49, 26, 52 } \) is replaced by 50, we first need to calculate the current mean of the set.
- Calculate the sum of the original set:
\[ 26 + 40 + 47 + 49 + 26 + 52 = 240 \]
- Count the number of elements in the set:
There are 6 elements.
- Calculate the current mean:
\[ \text{Mean} = \frac{\text{Sum}}{\text{Number of elements}} = \frac{240}{6} = 40 \]
- Replace one of the 26's with 50:
The new set will be \( { 50, 40, 47, 49, 26, 52 } \).
- Calculate the new sum:
\[ 50 + 40 + 47 + 49 + 26 + 52 = 264 \]
- Calculate the new mean:
\[ \text{New Mean} = \frac{264}{6} = 44 \]
- Compare the new mean to the old mean:
The original mean was 40, and the new mean is 44. Therefore, the mean has increased.
Conclusion: The mean would increase if the number 50 replaced one of the 26's in the set.