Answer:
The new mean will be 20.
Step-by-step explanation:
The Mean Value of a Data Set
The mean or average of a data set is found by adding all numbers and then dividing by the number of values in the set. Written as a formula:
[tex]\displaystyle \bar x=\frac{\sum x_i}{n}[/tex]
Where xi is the value of each data and n is the total number of values.
The mean of n=30 numbers is [tex]\bar x=18[/tex]. If each observation is increased by 2, then xi'=xi+2 and the new mean value will be:
[tex]\displaystyle \bar x'=\frac{\sum x'_i}{30}[/tex]
[tex]\displaystyle \bar x'=\frac{\sum x_i+2}{30}[/tex]
[tex]\displaystyle \bar x'=\frac{\sum x_i}{30}+\frac{\sum 2}{30}[/tex]
The sum of 30 times 2 is 60, thus:
[tex]\displaystyle \bar x'=18+\frac{60}{30}=18+2=20[/tex]
The new mean will be 20.
