Unit 1 Calculations

Symbols

100

What is the symbol for mean (sample and population)?

μ - population

x̄ - sample

200

What is the symbol for the standard deviation (sample and population)?

σ - population

s - sample

300

What are the symbols for sample and population size? What is the symbol for each individual unit?

n - sample size

N - population size

x_i - individual unit in a sample

400

What are the symbols for success and failure?

p - success

q - failure

500

What is the symbol for variance?

σ² - population

s² - sample

Calculator Steps

100

descriptive statistics

stat -> Calc -> 1-Varstat(data list)

200

probability table descriptive

Xlist:L1,p: L2. use L2 as freq list. Stat -> Calc -> 1-varstatL1, L2

300

Steps to find a binomial probability that is P(X=x).

2nd vars -> binomPDF(trials, p, value a)

400

! and combinations

math -> prob -> ! or nCr

500

Steps to find binomial distribution of P(X≤x).

2nd vars -> binomCDF(trials, p, value b)

Formulas

100

What are the formulas for sample mean?

x̄ = (Σx_i)/n

200

Write the formula for the z-score (sample and population).

Z = (x-μ)/σ - population

Z = (x-x̄ )/s - sample

300

Write the formulas for mean and standard deviation for a probability distribution.

μ = Σx * P (x) 

σ = √Σx_i²- p_i * μ² 

400

Write the formula steps to find the five-number summary and create a boxplot.

IQR = Q₃ - Q₁

STEP = 1.5 x IQR

Lower fence = Q₁ - step

Upper fence = Q₃ + step

500

What is the formula for the binomial distribution table?

P(x:n,p) = (nCx) p^x(q)^n-x 

R code

100

Command for the five number summary.

fivenum 

200

Code for boxplot.

boxplot(List1, List2, horizontal=TRUE, names = c("List1", "List2"))

300

What is the code for mean and weighted mean?

mean - mean

weighted.mean - weighted mean

400

What is the binomial probability of a single number?

dbinom(a, n, p)

500

What is the code for a binomial probability for a series of numbers?

sum(dbinom(a:b, n, p))

Random

100

What is discrete and continuous data?

Discrete variables can only take on a limited number of values (e.g., only whole numbers). Continuous variables can take on any value and any value between two values (e.g., out to an infinite number of decimal places).

200

What is parameter vs statistics?

A parameter is the measurement from the values of a population. A statistic is the measurement from the values of a sample.

300

What are the formulas for the mean and standard deviation of a binomial distribution?

μ = np

σ = √npq

400

How do you find the P(X>x)?

1 - binomcdf(n, p, b)

500

What is the difference between Bernoulli and binomial trials?

Bernoulli is one trial with success and failure and a given outcome. A Binomial is multiple Bernoulli trials that is a set number.