What happens to the median of a set of
data if you multiply each data value by the
same number?
nothig
Multiplying every value by a constant, will multiply median by that constant.
If you multiply each data value in a set by the same number, it will not affect the median. The median is the middle value in a sorted set of data. Multiplying each data value by the same number changes the scale of the data, but it does not change the relative order of the values.
To understand why the median is not affected, let's consider an example. Suppose we have the following set of data values: {2, 4, 6, 8, 10}. The median of this set is 6 because it is the middle value.
Now, let's multiply each value by 3: {2*3, 4*3, 6*3, 8*3, 10*3} = {6, 12, 18, 24, 30}. As you can see, the new set is {6, 12, 18, 24, 30}. The median of this set is still 18, because it is still the middle value.
In general, when you multiply each data value by the same number, it scales the entire data set uniformly, but it does not rearrange the values or change the relative position of the median. So, the median remains the same.