What is an assumed mean?

Answer 1

First of all, one needs to understand that this is another method of finding the Mean of a list of data. Sometimes the data is presented in a form which makes the calculation of the mean by the usual method impossible. Such a situation would involve a frequency table where the data is presented as an interval. For example, a question might be, "A person rolls a 1, 2 or 3 five times, then rolls a 4, 5 or 6 three times. What is the mean roll value?" Since we do not know exactly how many times each number has been rolled, we need another method to solve this problem. This would be an occasion to use an Assumed Mean. To solve the problem one chooses an arbitrary number which is close to the mean, in this case we could use 6 as the assumed value. Since it is an arbitrary choice, we could also use 5, or 2. It doesn't matter.

Next we set up a table as shown below

Dice value Frequency (f) Mid-Value (x) d = x - A fd A 1-3 5 2 -4 -20 6 4-6 3 5 -1 -3 8 -23 fd/f A + (fd/f) -2.875 3.125

We find the mid-value of each interval, and subtract the Assumed value (A) in this case 6, then we multiple that value (-4) times the frequency (5) to yield -20. Continue down the table. In the end, you add up your frequencies (8) and your f x d (-23), then divide fd by d. You then add this value to the assumed mean (6 + (-2.875)) and this is your mean 3.125! Easy once you know how.