Formula Card
Key of Variables and Notation
Σ means to sum what follows
𝑦" = estimate (prediction) of y
tα= t-score with probability of α to the
right
x = data value
µ = population mean
ME = margin of error
n = sample size
σ = population standard deviation
p0= hypothesized proportion
p = probability, population proportion, or pvalue
µ0 = hypothesized mean
𝑧!/# = z-score where 𝛼/2 is the area to the
right of z
p’= sample proportion = x/n, where
x is the number of successes
q = 1-p
sx = sample standard deviation of all x-values
df = degrees of freedom = n-1, for t
df = n-2, for r
α= significance level
st
nd
Q1, Q2, Q3 = 1 , 2 , and 3
rd
quartiles
Term
Formula/Notation
Calculator
Chapter 1
Random Integers
MATH > PRB > 5:randInt(min,
max, number of integers)
Chapter 2
Histogram, Scatterplot,
or Boxplot
Sample Mean
Sample Standard
Deviation
𝑥̅ =
∑"
#
∑(𝑥 − 𝑥̅ )$
𝑠= &
𝑛−1
2nd > StatPlot > 1 >
Histogram, Scatterplot or
Boxplot > Zoom > 9
Stat > Calc > 1-VarStats
Stat > Calc > 1-VarStats
Sample or Population
Variance
𝑠 $ 𝑜𝑟 𝜎 $
Range
Range = max - min
Interquartile Range
(IQR)
Potential Outliers
Interquartile range = Q3-Q1
-
Outliers = Above Q3+1.5*IQR or below Q1-1.5*IQR
Modified Boxplot (see above)
(Min, Q1, Med, Q3, Max)
𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑣𝑎𝑙𝑢𝑒 − 𝑚𝑒𝑎𝑛
𝑧-𝑠𝑐𝑜𝑟𝑒 =
𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑑𝑒𝑣𝑖𝑎𝑡𝑖𝑜𝑛 (𝜎, 𝑠, or s"̅ )
Stat > Calc > 1-VarStats
Five-Number Summary
z-Score
Stat > Calc > 1-VarStats &
then VARS > then 5 > and then
3 for sample or 4 for population
> and then press the 𝑥! key
-
-
Empirical Rule
68% within 1s, 95% w/in 2s, and 99.7% w/in 3s
-
kth Percentile
average of values above and below i = k/100(n+1)
-
Probability of Event A
Complement of Event A
Addition Rule
Conditional Probability
Independence Tests
Chapter 3
# 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑖𝑛 𝐴
𝑃(𝐴) =
𝑡𝑜𝑡𝑎𝑙 # 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 𝑖𝑛 𝑒𝑛𝑡𝑖𝑟𝑒 𝑆𝑎𝑚𝑝𝑙𝑒 𝑆𝑝𝑎𝑐𝑒
𝑃(𝐴′) = 1 − 𝑃(𝐴)
𝑃(𝐴 𝑂𝑅 𝐵) = 𝑃(𝐴) + 𝑃(𝐵) − 𝑃(𝐴 𝐴𝑁𝐷 𝐵)
𝑃(𝐴 𝐴𝑁𝐷 𝐵)
𝑃(𝐴 | 𝐵) =
𝑃(𝐵)
𝑃(𝐴 | 𝐵) = 𝑃(𝐴)
-
𝑃(𝐴 𝐴𝑁𝐷 𝐵) = 𝑃(𝐴) ∙ 𝑃(𝐵)
Multiplication Rules
𝑃(𝐴 𝐴𝑁𝐷 𝐵) = 𝑃(𝐴) ∙ 𝑃(𝐵) ∗∗∗ 𝑖𝑓 ∗∗∗
-
𝐴 𝑎𝑛𝑑 𝐵 𝑎𝑟𝑒 𝑖𝑛𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡.
𝑃(𝐴 𝐴𝑁𝐷 𝐵) = 𝑃(𝐴 | 𝐵) ∙ 𝑃(𝐵), 𝑎𝑙𝑤𝑎𝑦𝑠.
Chapter 4
Mean of Discrete
Probability Distribution
𝜇 = Q 𝑥 ∙ 𝑃(𝑥)
Stat > Calc > 1-VarStats L1, L2
where L1 is x and L2 is P(X)
Standard Deviation of
Discrete Probability
Distribution
Binomial Probability
s = RQ(𝑥 − 𝜇)$ ∙ 𝑃(𝑥)
P(x = a) =
# 𝐶&
∙ 𝑝& ∙ 𝑞#'&
(I would always use binompdf & binomcdf instead.)
Mean & Standard
Deviation of Binomial
Probability
Probability, Given z
Stat > Calc > 1-VarStats L1, L2
where L1 is x and L2 is P(X)
2nd > DISTR > binompdf(n, p,
exact number) or
binomcdf(n, p, this number or
fewer)
𝜇 = 𝑛∙𝑝
s = X𝑛 ∙ 𝑝 ∙ (1 − 𝑝)
Chapter 6
Table A
z, Given Probability to
left
Table A
x, Given Probability to
left
𝑥 = 𝜇+𝑧∙𝜎
2nd > DISTR > normalcdf(min,
max, mu, 𝜎 or 𝜎% )
√𝑛
2nd > DISTR > invNorm(area
to left, mu, 𝜎 or 𝜎% )
√𝑛
2nd > DISTR > invNorm(area
to left, mu, 𝜎 or 𝜎% )
√𝑛
Chapter 7
Mean of Sampling
Distribution: Means
Standard Deviation
(Error) for Sample
Means
-
𝜇"̅ = 𝜇
𝜎
s"̅ =
√𝑛
or
𝑠
-
√𝑛
Chapter 8
Standard Deviation
(Error) for Sample
Proportions
Margin of Error:
Proportions
Margin of Error: Means
Confidence Interval:
Proportions
Confidence Interval:
Means
Sample Size:
Proportions
Sample Size: Means
z-Score: Proportion
t-Score: Mean
s() = &
-
𝑝′(1 − 𝑝′)
𝑛
𝑝′(1 − 𝑝′)
𝑀𝐸 = 𝑧&
𝑛
𝑠
s
𝑀𝐸 = 𝑡 ∙
= 𝑧∙
√𝑛
√𝑛
𝑝′(1 − 𝑝′)
𝐼𝑛𝑡𝑒𝑟𝑣𝑎𝑙 = 𝑝′ ± 𝑧&
𝑛
𝑠
𝐼𝑛𝑡𝑒𝑟𝑣𝑎𝑙 = 𝑥̅ ± 𝑡 ∙
√𝑛
𝑝′(1 − 𝑝′)𝑧 $
𝑛­ =
𝑚𝑒 $
𝑛­ =
*!+ !
,- !
or
.!+ !
Stat > Tests > 1-PropZInt
Stat > Tests > TInterval (or
zInterval if σ is known)
-
,- !
Chapter 9
𝑝′ − 𝑝/
𝑧=
R𝑝/ (1 − 𝑝/ )
𝑛
"̅ '0
"̅ '0
𝑡 = .⁄ " or 𝑧 = s⁄ "
√#
-
√#
Stat > Tests > 1-PropZTest
Stat > Tests > T-Test (or
zTest if σ is known)
Chapter 12
Correlation
r
Stat > Calc > 4: LinReg
Coefficient of
Determination
Residual
r2
Stat > Calc > 4: LinReg
Regression Line
𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙 = 𝑦 − 𝑦`
𝑦` = 𝑎𝑥 + 𝑏
Stat > Calc > 4: LinReg