MATH135

Geometric mean

$$\sqrt{x\cdot x\cdot x...}$$

Variance

$$\sigma^2=\frac{1}{n-1}\sum\left(x_{i}-x_{av}\right)^2$$

Standard deviation

$$\sqrt{\sigma}$$

One mode is called what? 2 modes? And more than two modes?

Unimodal, bimodal,multimodal

Harmonic mean

$$\frac{n}{\frac{1}{x_1}+\frac{1}{x_2}+...\frac{1}{x_{n}}}$$

Histogram

Showing frequency distribution for numerical data. Has intervals (bins)

Scatter Plots

Shows the relationship between two variables

Bar chart

Best used for categorical data (like fav colors). Shows frequency data.

Linear regression

$$y=mx+b$$

Residuals in linear regression

When the y coordinate of a data point minus the linear regression y coordinate (predicted)y_{\imaginaryI}-y_{predicted}

Interpolation

Finding an x value that lies within the range of observed data points. Plugging it in.

Extrapolation

Finding an x values that lies outside the range of observed data points.

Correlation coefficient

If p is greater than 0.7 correlation is strong, if p is less than 0.5 correlation is weak, p will be moderate if it’s between 0.5, and 0.7

Exponential function

$$y=b\cdot a^{x}$$

Population growth

$$P(t)=P_0\cdot e^{rt}$$

Radioactive decay

$$N(t)=N_0\cdot e^{-kt}$$

$$a^{y}=x$$

$$\log_{a}x=y$$

$$\log_{a}(a)=$$

1

$\log_{a}(x)$ change of base formula,base 10

$$=\frac{\log_{10}(x)}{\log_{10}(a)}$$

change of base formula base e

$$\log_{a}(x)=\frac{\ln(x)}{\ln(a)}$$

$\lim_{x\to\infty}a_{n}=L$ describe converagnces (4)

An = 1/n converges to 0

An = [(-1)^n] /n converges to 0 oscilary

An= N diverges to +infinity

An= (-1)^n oscillates and doesn’t converge

Geometric sequence equation

$x_{n+1}=r\cdot x_{n}$ Where n is term

General solution of geometric sequence

$$x_{n}=r^{n}\cdot x_0$$

Behavior if geometric sequence 4

$0<r<1$ converges

$-1<r<0$ converges

$r\le-1$ diverges

$r>1$ diverges

Semi-Log Plott

X to In(y) axis

Log-Log Plott

in(y) by in(x)