Question

Whats the most easiest way to find the mean...of a dot plot

Answer 1

"Easiest" depends on several factors, including your understanding of what you're trying to do and of how the mean is calculated.

The most straight-forward way is to

1. multiply the value of a column by the number of dots in that column
2. add the products
3. divide by the total number of dots

One of my favorite ways is this.

1. Choose a value near the middle of the plot and call it the (provisional) mean. Often, I will choose a value that has the most dots, or that has dots fairly symmetrically distributed around it.
2. Match dots that are symmetrically located around that mean and cross them off. That is, for every dot that is 1 unit above the (provisional) mean, cross off it and a dot that is 1 unit below the (provisional) mean. (With some experience, you can recognize non-symmetrical dots that can cancel. For example, one that is +2 and one that is +3 together will cancel one that is -5.)
3. For the dots left over, multiply the number of dots by their distance from the (provisional) mean, and add the products. Most likely, some will be positive, some will be negative.
4. Divide the total from the previous step by the total number of dots. Add that (signed) result to the provisional mean. This gives the true mean.

If the distribution is reasonably symmetrical, this second method gives you fewer (and smaller) products to compute, and you can probably do them in your head.