Problem: The mean of 16 numbers is 8. If 2 is added from every number, what will be the new mean?

Solution:

We can solve this problem using the following formula:

New Mean = (Sum of New Values) / (Number of Values)

To find the new mean, we need to first find the sum of the new values. Since we are adding 2 to every number, the sum of the new values will be:

Sum of New Values = (Sum of Original Values) + (2 * Number of Values)

where the "Number of Values" is 16 in this case.

We know that the original mean is 8, so we can find the sum of the original values using the formula:

Sum of Original Values = (Original Mean) * (Number of Values)

Substituting the given values, we get:

Sum of Original Values = 8 * 16 = 128

Now, we can use the formula for the sum of new values:

Sum of New Values = 128 + (2 * 16) = 160

Finally, we can use the formula for the new mean:

New Mean = (Sum of New Values) / (Number of Values) = 160 / 16 = 10

Therefore, the new mean is 10.

Explanation:

To find the new mean after adding 2 to every number, we need to first understand the formula for the mean. The mean is calculated by adding all the values and dividing the sum by the number of values. In this case, we are adding 2 to every number, so we need to adjust the sum accordingly.

We can use the formula for the sum of new values to find the new sum after adding 2 to every number. Once we have the new sum, we can use the formula for the new mean to find the answer.

It is important to note that adding a constant value to every number will not change the variance or standard deviation of the data. Only the mean will change.

Given,  there are 16 numbers Mean = 8.Let their sum be x. So mean = x/16 =8. If two is added to each number then the  sum increases by 16*2 = 32.So, for finding the new mean we'll divide it  by 16 ∴ Mean = (x+32)/16 ⇒ 8+2 =10. So, the required new mean is 10.