So a lot of these measurements you've gone over in some kind of basic math class, but they're also important in Biology, and specifically, genetics, because genetics uses these measurements to analyze phenotypes. Generally, this is a sample of a phenotype, a phenotype in an entire population, or a phenotype across all organisms in the world. But in order to analyze those large numbers of phenotypes, we have to be able to quantify them and say, "this phenotype differs from this one by this much." I'm going to introduce some measurements which you are likely familiar with from some math class, but I just want to present them in the way of genetics. So the first is the mean, which is an average. There are two types of means that we can take in genetics. One is the population mean, which is all individuals within the group that you're measuring, like all humans in Florida or all sloths in Costa Rica. Typically, the mean is studied in the form of a sample, a representative subset instead of the entire population. For instance, we take 30 humans from each continent instead of all humans on Earth. However, using a sample must be approached with caution because you could accidentally select individuals who don't represent the broader population.

The way you calculate the mean is represented by this formula: Σi=1nxi which stands for sum, and you're adding all measured values (denoted xi) then dividing by the number of individuals. For instance, if measuring the tail length of 100 lizards, sum the tail lengths and divide by 100. Another important measure is variance, which indicates how far individual observations are from the mean. The variance formula is given by s2=Σi=1n(xi-μ)2n-1 where μ is the mean value.

Standard deviation is another common statistic, which measures the amount of variation in a set of data. It is the square root of variance. The formula for standard deviation is: s=Σi=1n(xi-μ)2n-1. A related concept is standard error, which measures how accurate the sample mean is compared to the entire population. A lot of these values can be depicted on a normal distribution or a bell curve, showing how data points spread away from the mean.

Each value in this histogram represents a percentage of the population that falls within certain ranges, which helps in understanding how traits vary within a population. Variance in this context can be illustrated by the spread of the curve; narrower curves indicate low variance, and wider curves indicate high variance. Understanding these statistics helps analyze genetics, among other fields, by quantifying characteristics and making comparisons possible.