Calculating the Included Number from Mean Change
The problem asks for the value of a number added to a set, given the change in the mean.
Initial Sum Calculation
We are given that the mean of 6 numbers is 18. The sum of these 6 numbers can be calculated using the formula:
$ \text{Sum} = \text{Mean} \times \text{Count} $
So, the sum of the initial 6 numbers is:
$ \text{Sum}_{6} = 18 \times 6 = 108 $
New Sum Calculation
When one more number is included, the total count becomes 7. The new mean is given as 20. The sum of these 7 numbers is:
$ \text{Sum}_{7} = 20 \times 7 = 140 $
Finding the Included Number
The number that was included is the difference between the sum of the 7 numbers and the sum of the initial 6 numbers.
$ \text{Included Number} = \text{Sum}_{7} - \text{Sum}_{6} $
$ \text{Included Number} = 140 - 108 = 32 $
Therefore, the number included is 32.
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