You want to know how many decimal places are in the total number of M&Ms in your bowl, but there’s no way to count them all without getting sick from eating too many!
So instead, you take a sample and count the number of M&Ms in that small group. Let’s say you choose 100 M&Ms at random and count how many are red (because we love those bright colors). You might find that there are 35 red M&Ms out of your total 1,200 M&Ms.
Now, let’s translate this into math terms. The number of red M&Ms is our sample size (in this case, it’s 35), and the total number of M&Ms in the bowl is called the population (which is 1,200). To find out how many decimal places are in that population, we need to calculate something called the standard error.
The formula for calculating the standard error looks like this:
standard error = square root of [(population variance) / (sample size)]
In our M&M example, let’s say there are 10 different colors and each color has an equal number of M&Ms in the bowl. If we assume that every color is equally likely to be chosen for our sample, then the population variance would be:
population variance = (number of red M&Ms average number of all M&Ms) squared + (number of green M&Ms average number of all M&Ms) squared + … + (number of yellow M&Ms average number of all M&Ms) squared
In this case, the population variance would be:
population variance = [(35-120/10)^2 + (40-120/10)^2 + … + (20-120/10)^2] / 10
To find out how many decimal places are in the population, we need to calculate the standard error using this formula:
standard error = square root of [(population variance) / (sample size)]
If our sample size is large enough and our population variance is relatively small, then the standard error will be very close to zero. This means that there are no decimal places in the population! On the other hand, if our sample size is small or our population variance is high, then the standard error will be larger and we’ll need more decimal places to accurately represent the population.
So basically, when you hear someone talking about “maximum decimal places” in math, they’re just trying to figure out how many digits are needed to accurately describe a large group of numbers (like all the M&Ms in your bowl). And if you ever find yourself struggling with this concept, just remember that it’s like counting red M&Ms and then using some fancy math formulas to make sure you didn’t miss any!