The mean of a set of 51 data points is 3.04. If a data value of 16 were added to the data set, what would be the approximate value of the new mean?
Mean = Σx/n
3.04 = Σx/51
Solve for Σx, then
Mean = (Σx+16)/(n+1)
To find the approximate value of the new mean after adding a data value of 16, we need to use the formula for calculating the mean:
Mean = (Sum of all data points) / (Number of data points)
Given that the mean of the original set of 51 data points is 3.04, we know that the sum of all the data points is 51 * 3.04 = 155.04.
Now, to find the approximate value of the new mean after adding the data value of 16, we need to calculate the new sum of all the data points. Since we added one more data point, the new sum will be the original sum (155.04) plus the value of 16.
New sum of all data points = 155.04 + 16 = 171.04
Finally, to find the new mean, we divide the new sum of all data points by the new number of data points, which is 51 + 1 = 52.
Approximate value of the new mean = 171.04 / 52 ≈ 3.29
Therefore, the approximate value of the new mean, after adding a data value of 16, is 3.29.