Many things in nature, like heights or test scores, follow a "Normal Distribution," or Bell Curve. Let's gather some "Stat-berries" from the mountain and see where they land!
Most berries land near the middle (the mean, or average). As you get further from the middle, there are fewer and fewer berries. That's a Normal Distribution!
Standard Deviation (SD) measures how "spread out" data is from the average (mean). A low SD means data is tightly clustered, while a high SD means it's spread far apart.
Fish are tightly packed.
Fish are very spread out.
River A is more predictable! Because the fish (data points) are less spread out, it has a Lower Standard Deviation. You'd know almost exactly where to cast your line. In River B (High SD), the fish are all over the place!
A Z-Score tells us how many standard deviations a single data point is away from the mean (average). It's a measure of "uniqueness"!
The average villager height is 170cm.
The standard deviation is 5cm.
A new explorer, Biff, arrives.
Their height is 180cm.
Biff's height is 10cm from the average (180 - 170). Since one standard deviation is 5cm, Biff is 2 Standard Deviations away from the mean.
Z-Score = (180 - 170) / 5 = 2.0
A Z-score of 2 (or -2) or more is generally considered "unusual" or statistically significant. Biff is quite tall for this village!
Correlation shows if there is a relationship between two variables. But beware! Correlation does NOT equal causation!
As the temperature goes UP, ice cream sales also go UP. The dots trend upwards from left to right.
Important: Does this mean ice cream sales cause the temperature to rise? Of course not! A third factor (hot, sunny weather) causes both.