What is the difference between mean, median and mode?
The mean is the total divided by the count. The median is the middle value once sorted. The mode is the value occurring most often. For 2, 3, 3, 4, 88 the mean is 20, the median is 3 and the mode is 3 — and the mean is arguably the least useful of the three here, because one large value has dragged it away from everything else in the set.
When should I use the median instead of the mean?
Whenever the data is skewed or contains outliers. Income, house prices and response times are all reported as medians for this reason: a handful of extreme values distorts the mean while barely moving the median. If mean and median differ noticeably, that gap is itself informative — it tells you the distribution is lopsided and a single average is hiding something.
Can a data set have more than one mode?
Yes. Two values tied for most frequent makes it bimodal, more than two multimodal, and if every value appears once there is no mode at all. Bimodality often signals two different groups mixed together — a bimodal distribution of test scores may mean one cohort understood the material and another did not, which is far more useful than any single average.
What is a weighted average and when do I need one?
When the values do not all count equally. A course grade where the exam is worth 50% and homework 20% needs a weighted mean: multiply each score by its weight, sum, divide by total weight. Using a plain average of 85 and 75 gives 80, but if the 75 carries most of the weight the true figure is much closer to 75. Any time inputs represent different sizes or importance, a plain mean is wrong.
What is the range, and why is it not enough?
The range is the largest value minus the smallest — a quick measure of spread. Its weakness is that it depends entirely on two extreme values and ignores everything between them. Two data sets can share a range while being distributed completely differently. Standard deviation is more informative because it accounts for every value's distance from the mean.
Does the average tell me what is typical?
Not necessarily, and this is the practical trap. The mean of a bimodal set can be a value that never occurs and is not typical of anything. Averages of counts can be impossible in reality — the average household having 1.8 children. Always look at the spread alongside the average; a mean without any measure of variability can be actively misleading.