The tenth value is 15
Solution:
Given that, data set has 9 values
The mean of the set is 5
Number of values = 9 and mean = 5
The mean is given by formula:
[tex]mean = \frac{\text{Sum of terms}}{\text{Number of terms}}[/tex]
[tex]5 = \frac{\text{Sum of 9 terms}}{9}\\\\sum\ of\ 9\ terms = 5 \times 9 = 45[/tex]
When a tenth value is added, the mean becomes 6
Let the tenth value be "x"
New mean is given as:
[tex]6 = \frac{\text{sum of 9 terms} + x}{10}\\\\sum\ of\ 9\ terms + x = 60[/tex]
The tenth value is given as:
sum of 9 terms + x = 60
45 + x = 60
x = 60 - 45
x = 15
Thus the tenth value is 15
