A data set has nine values. The mean of the set is 5. When a tenth value is added, the mean becomes 6. What is the tenth value?
The mean of a data set is found by finding the sum of all the values and dividing by the number of values.
Therefore, the sum of all the values must be the mean times the number of values.
Since the mean is 5 and there are 9 values, the sum of these numbers must be 5 x 9 or 45.
When a tenth value is added and the means becomes 6, the sum of these numbers must be 6 x 10 or 60.
Therefore, the tenth value must be 60 - 45 or 15.