Question

Look at this set of 6 numbers:
26n40 47 49 26 52
How would the mean change if the number 50 replaced one of the 26's in the set?
increase,decrease,no change

Answer 1

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.

1. **Calculate the sum of the original set:**

\[
26 + 40 + 47 + 49 + 26 + 52 = 240
\]

2. **Count the number of elements in the set:**

There are 6 elements.

3. **Calculate the current mean:**

\[
\text{Mean} = \frac{\text{Sum}}{\text{Number of elements}} = \frac{240}{6} = 40
\]

4. **Replace one of the 26's with 50:**

The new set will be \( \{ 50, 40, 47, 49, 26, 52 \} \).

5. **Calculate the new sum:**

\[
50 + 40 + 47 + 49 + 26 + 52 = 264
\]

6. **Calculate the new mean:**

\[
\text{New Mean} = \frac{264}{6} = 44
\]

7. **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.**