statistics

What are the 3 measures of center?

Mean, median and mode

What are the four measures of spread?

Standard deviation, Variance, IQR and Range

When will the standard deviation be zero?

When all the values are the same

Interpret the standard deviation

The typical distance from the data to the Mean

Right Skewed VS left Skewed

Right Skewed Has a tail on the right with the Mean larger than the median. Left skewed Has a tail on the left with a media Larger than the mean

Outlier test

LB: Q1- 1.51QR

UB: Q3+ 1.51QR

Describe a distribution

Shape, outliers, Center and spread

What are the summary statistics that are resistant to ourliers?

Media and IQR

What are the summary statistics that are non-Resistant to outliers?

Mean, standard deviation and range

Percentiles

Z=x-ų/ õ

Standard normal distribution

N(0,1)

What do the numbers 68-95-99.7 mean?

Empirical rule in a normal distribution 68% of all data is within one standard deviation of the Mean 95% is within to standard deviations And 99.7% is within three standard deviations

What is the main difference between segmented bar graph and A mosaic plot?

a mosaic plot Takes the simple sizes Of the explanatory variable into account by the distribution on the X axis

Correlation coefficient

R Determines The strength of a linear relationship between X and Y

What three things does the value of r communicate?

Linear form, direction and strength

Coefficient of determination

r² Is the percent of the variability in why that can be explained by the LSRL of the Y on X

Describe a scatter plot

Form(linear or exponential) Association(positive Or negative) Strength(Strong, moderate or weak) and any outliers

Residual

Observed y Predicted x

What does the LSRL minimize?

The square of the Residual, the vertical distance from the lines to the points

Interpret the Y intercept

The predicted value of Y when x is zero

Interpret the slope

For every one increase in x, We predict a slope in increase y

What are the four sources of bias in a Study?

Undercoverage, No response respond Bias and hiding bias

What are two biased sampling methods?

Voluntary response and convenience Sample

What is the difference between a cluster sample and a stratified sample?

A cluster sample splits the population into heterogeneous groups and then an SRS is used to select the clusters. a stratified sample split the population into homogeneous groups and then an SRS is taken from strata.

Why do we block in experiments?

It reduces variation in the treatment groups

Matched Pairs Experiment

All subjects receive both treatment

Why do we randomize in experiment?

It reduces the effect of variables that we might not know about

What is the main difference between an experiment and an observational study?

A treatment is applied in an experiment

What are the four principles of experimental design?

Randomization, replication, control and comparison

What is the scope of different for experiments and studies?

If the data was collected using random selection, you can make inference about the population, if the data was analyze using random assignment, you can make inference for cause and effect

What does it mean when two events are mutually Exclusive?

They have no outcomes in Common

General audition rule

P(A or B)= P(A)+ P(B)-P(A and B)

General multiplication rule

Independent: P(A and B)= P(A)* P(B)

Dependent: P(A and B)= P(A)* P(B/A)

what does it mean when two events are independent?

One event does not affect the probability of the other event

How can you test if two events are independent?

P(A and B)= P(A)* P(B)

P(A/B)= P(A)

Expected value of a discrete random variable

Mx= E(X)= X1* P1+ x2+p2+… XN* PN

Standard deviation of a discrete, random variable

Ōx= Square root(xi-ųx)²*pi

Adding And subtracting random variables

That means get added or subtracted. You only add the variances and take the square root to get the standard deviation.

Linear transformation of a random variable

E(a+bx)= a+bE(X)

Var(b Eggs