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Formulas for the Final Exam
Five number summary
Minimum
Q1
Median
Q3
Maximum
InterQuartile Range : IQR  Q 3  Q1
Range  Maximum  Minimum
Mean
x
x
n
y
y
n
S tandard Deviation
sx 
sy 
  x  x 2
n 1
  y  y 2
n 1
S tandardized S core
zx 
xx
sx
zy 
y y
sy
Correlation Coefficient
z x z y   x  x  y  y 

r

n  1s x s y
n 1
S lope
br
sy
sx
Intercept
a  y  bx
Prediction Equation
yˆ  a  bx
residual  y  yˆ
R 2  r 2
1
Sampling Distribution of p̂ :
np  15 and n1  p  15
Sampling Distribution of y :
Shape: normal if population
has a normal shape, otherwise
approximately normal
Mean: p
Mean: μ
Shape: Approximately normal if
Standard Deviation: SD pˆ  
p1  p 
n
Standard Error: S E y  
s
n
Single sample (Categorical Variable)
Confidence interval for p :
pˆ  z *
pˆ 1  pˆ 
to pˆ  z *
n
Confidence
z*
Test Statistic:
pˆ 1  pˆ 
n
80%
1.282
z
90%
1.645
95%
2 or 1.96
pˆ  po
p0 1  p0 
n
98%
2.326
99%
2.576
Single sample (Numerical Variable)
Confidence interval for μ:
y  t*
s
s
to y  t *
n
n
Test Statistic:
df = n – 1
t
y  o
s
n
df = n – 1
Two independent samples (Numerical Variable)
Confidence interval for
(̅
̅ )
√
:
(̅
̅ )
Test Statistic:
√
(̅
̅ )
√
df = nasty formula so this will be provided for you or given in JMP
2
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