1 ⎛ N-1 ⎞
x̅ = ─── ⎜ ∑ xᵢ⎟
N ⎝ i=0 ⎠
There are many kinds of 'mean'-s.
Average is arithmetic mean.
https://www.cuemath.com/data/difference-between-average-and-mean/
A measure of 'spread' of data.
aka σ, s, SD
⎡ 1 ⎛ N-1 ⎞⎤
σ² = ⎢─── ⎜ ∑ (xᵢ - μ)²⎟⎥
⎣ N ⎝ i=0 ⎠⎦
--------------------------
/ ⎡ 1 ⎛ N-1 ⎞⎤
σ = / ⎢─── ⎜ ∑ (xᵢ - μ)²⎟⎥
√ ⎣ N ⎝ i=0 ⎠⎦
σ² is variance.
To get the value of the same unit as the xᵢ values, we take the square root of σ², which is the standard deviation σ.
Most frequently occurring value.
Eg:
In
10, 23, 42, 23, 20, 24, 19, 39, 24, 28, 24
24 is mode.
DOUBT: What if there are multiple values which occur most frequently?
https://www150.statcan.gc.ca/n1/edu/power-pouvoir/ch11/mode/5214873-eng.htm
The middle value when the values are arranged from smallest to largest.
From Britannica:
(mean, mode and median are) the three principal ways of designating the average value of a list of numbers.
DOUBT: How can we get average value from median or mode?
From Spiegelhalter's popsci book:
any process of fitting lines or curves to data
Difference (or error) of a point from the line: residual
Response variable:
Explanatory variable:
The gradient/slope of the regression curve/line: regression coefficient
| Type I error | False positive |
| Type II error | False negative |
In a classification problem.
Error matrix aka confusion matrix.
A process where next state depends only the current state.
'Future is independent of the past' in some sense. ˡ
Useful for data where growth/decline is exponential.