Statistics for Chemical Analysis

mean

/ meen /

Suppose four classmates split a pizza and you want one number to describe how big each slice was. You add up the slices and divide by four. That single, fair-share number is the mean: the everyday average. In the lab it is the first thing you compute when you have measured the same thing several times.

The mean of a set of measurements is their sum divided by how many there are. If you titrate the same sample five times and get five slightly different volumes, the mean is your best single estimate of the true value, because the random ups and downs of individual readings tend to cancel out when you add them together.

It matters because no single measurement is perfectly trustworthy, but the mean of many is steadier and closer to the truth. The honest caveat is that the mean is easily dragged off course by one wildly wrong reading: a single outlier can pull the average noticeably, which is why chemists also look at the spread and sometimes at the median.

Five replicate titrations give 24.98, 25.02, 25.00, 24.96 and 25.04 mL. Their sum, 125.00 mL, divided by five gives a mean of 25.00 mL, reported as the best estimate of the endpoint volume.

Averaging replicate titration volumes to get one best estimate.

The plain word average usually means this arithmetic mean, but median and mode are also kinds of average; in analytical chemistry mean almost always refers to the arithmetic mean.

Also called
averagearithmetic mean算术平均值算術平均值均值