If every value in the data set is increased by a constant k, the mean, median, and mode of the new data set can be found by adding k to each of the original statistics.
We want to find the mean, median, mode, range, and standard deviation of the data set in which each value is increased by a constant k= 25.
Let's start by writing initial data set of size n in the increasing order.
x_1, x_2, ..., x_n
Now, we can write the transformed data set.
x_1+ 25, x_2+ 25, ..., x_n+ 25
If every value in the data set is increased by the constant 25, then the statistics of the new data set will behave in a consistent, predictable way.
The new mean, median, and mode can be found by adding 25 to the mean, median, and mode of the original data set.
The range and standard deviation will not change.
Notice that only the measures of center are increased by the constant and the measures of variation will not change. This is because the distances between the individual values do not change.
Adding a Constant
Finally, we can find new values of the statistics by adding 25 to the mean, median, and mode.
