Answer: Let's assume the smallest term in the data set is represented by "x," and the greatest term is represented by "y."
According to the given information, the smallest term is 20% of the greatest term, which can be written as:
x = 0.2y
The range of the data is the difference between the greatest and smallest terms, which is given as 320:
Range = y - x = 320
Now, we can use the first equation to solve for x in terms of y and then substitute it into the range equation:
x = 0.2y
Range = y - 0.2y = 0.8y
Now, we know that the range is 320, so we can set up the equation:
0.8y = 320
To find the value of y, divide both sides by 0.8:
y = 320 / 0.8
y = 400
Now that we know the greatest term (y = 400), we can find the smallest term (x) using the equation x = 0.2y:
x = 0.2 * 400
x = 80
So, the smallest term in the data set is 80.