Final answer:
To calculate the new mean after adding a data value of 6 to the original 38 data values with a mean of 5, you first find the total sum of the original data, add the new data value, and then divide by the new number of data points to get a mean of approximately 5.026.
Step-by-step explanation:
To calculating the new mean when an additional data point is added to an existing dataset with 38 values and an existing mean of 5. To find the new mean, you first multiply the original mean by the number of data points to find the sum of all the original data values:
Original Total Sum = Mean × Number of Data Points = 5 × 38 = 190
Then add the new data value to this sum:
New Total Sum = Original Total Sum + New Data Value = 190 + 6 = 196
Now, divide the new total sum by the new number of data points to find the new mean:
New Mean = New Total Sum / New Number of Data Points = 196 / 39
Thus, the new mean is approximately 5.026.