The mean of a data set is equal to 10 and its standard deviation is equal to 1. if we add 5 to each data value, then the mean and standard deviation become
a. mean = 15 , standard deviation = 6
b. mean = 10 , standard deviation = 6
c. mean = 15 , standard deviation = 1
d. mean = 10 , standard deviation = 1

Let
S = sum of the data values
n = number of data values

The mean M is equal to 
M = S/n
since you add up the values and divide by n. We don't need to know what S or n are. 

If we add 5 to each data value, then we're adding on n copies of 5, or 5n

The new mean N is

N = (S+5n)/(n)
N = (S/n) + (5n/n)
N = M + 5

The new mean is a result of taking the old mean M and adding on 5

So,
N = M+5
N = 10+5
N = 15

The standard deviation will remain the same because each data value hasn't moved in relation to one another. Every data value has been shifted up the same amount. For instance if A and B are two points in this data set, then A+5 and B+5 will be the same distance away. Apply this logic to any number of data values. While standard deviation isn't that simple, it still has a loose connection to "distance" of the values, or how spread out they are. 

So that's why the final answer is choice C)