I'm really not good in math, please bear with me. I searched and found some questions which are similar to this question. However, I cannot understand them. I get doubt in this question for a day. It's quite easy but I don't know.
If I have 3 boxes, and I put tickets into them. For example, three boxes are put 1, 3, and 2 tickets respectively.
How can I find the average, variance, and mode of boxes?
Thank you for your help.
The average is just the sum of the number of tickets in each box and divide by the number of boxes:
$$\frac{\sum\limits_{i=1}^n{x}}{n} = \frac{1+2+3}{3} = 2 = \mu$$
The variance is:
$$\frac{\sum\limits_{i=1}^n{(x-\mu)^2}}{n} = \frac{(-1)^2 + 0^2 + 1^2}{3} = 0.666$$
The mode is the value that occurs more times. When all values occur the exact same times, we have an amodal data (your case).