Calculate the Average Change: Adding 1 to the Set {2,3,4,5}

Question

Look at the following numbers:

2,3,4,5 2,3,4,5

If we add the number 1 to the group, then how will the average change?

Video Solution

Step-by-Step Solution

To solve this problem, we'll begin by calculating the average of the original group of numbers (2,3,4,52, 3, 4, 5):

1. Calculate the sum of the original group: 2+3+4+5=142 + 3 + 4 + 5 = 14.

2. Determine the number of elements in the original group: 44.

3. Calculate the average of the original group: 144=3.5\frac{14}{4} = 3.5.

Next, we'll calculate the average after adding the number 11 to the group, forming the new group (1,2,3,4,51, 2, 3, 4, 5):

1. Calculate the sum of the new group: 1+2+3+4+5=151 + 2 + 3 + 4 + 5 = 15.

2. Determine the number of elements in the new group: 55.

3. Calculate the average of the new group: 155=3\frac{15}{5} = 3.

Finally, compare the two averages:

The average of the original group is 3.53.5, while the average of the new group is 33.

The average decreases when the number 1 is added to the group.

Therefore, the solution to the problem is that the average will decrease.

Answer

It will decrease.