Look at this set of 6 numbers:

Question

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.