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TI 83/84 Statistics Summary – Formulas
Sample Mean
Sample Standard Deviation
Formula
Where:
Sxi
x= n
S
means sum (add)
Formula
x is the sample mean
xi is each of the
observed values
Population Mean
Formula
Where:
Sxi
m= N
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n is the sample size
(number of observations)
s=
Where:
S
means sum (add)
x is the sample mean
S(xi – x)2
n-1
xi is each of the
observed values
or
n is the sample size
(number of observations)
Sxi2 – (Sxi)2/n
s is the Sample Standard
n-1
Deviation
(computational formula)
s=
S
means sum (add)
m is the sample mean
Population Standard Deviation
xi is each of the
observed values
Formula
N is the population size
(number of observations)
Mean of a Discrete Random Variable
Formula:m = SxP(X=x)
Where: x is each of the
observed values
P(X=x) is the probability
of the observed value
s=
Where:
S(xi – m)2
N
or
S
means sum (add)
Formula:m = np
Formula: s =
S(x – m)2 P(X=x)
Formula: s =
Sx2 P(X=x) – m2
Definition: Middle value in ordered list
• If the number of observations is odd, the
median is the middle number
• If the number of observations is even, the
median is the mean of the two middle
numbers
or
(Computational
formula)
x is each of the
observed values
P(X=x) is the probability
of the observed value
• Arrange the data in increasing order
Quartiles
Definition: Divide the values into 4 sets with an
(approximately) equal number of members
Arrange the data in increasing order and determine
the median
• 1st Quartile – Throw away all values above
the median. 1st Quartile is the median of the
remaining data
• 3rd Quartile – Throw away all values below
the median. 3rd Quartile is the median of the
remaining data
Mean of a Discrete Random Variable
Median
Definition: Range = Max - Min
xi is each of the
observed values
N is the sample size
(number of observations)
Where:
Range
• 2nd Quartile – Median of the original data set
Sxi2
s=
s is the Population
– m2
N
Standard Deviation
(computational formula)
p is the probability
of success
Definition: Most frequent value(s)
m is the sample mean
Mean of a Binomial Random Variable
Where: n is the number of
trials (outcomes)
Mode
m is the mean
Interquartile Range (IQR)
Definition: IQR = Q3 – Q1
Five-Number Summary
Definition: Min, Q1, Q2, Q3, Max
Lower and Upper Limits
Definition: Lower Limit = Q1 – 1.5 * IQR
Upper Limit = Q3 + 1.5 * IQR
Outliers
Definition: Data values below the lower limit or
above the upper limit
z-Score (standard score)
Std. Dev. of a Binomial Random Variable
Meaning: z-Score tells the number of standard
deviations an observed value is from the mean
Formula:m =
Formula
np(1-p)
n is mean
p is prob. of success
z=
x–m
x–x
s
z=
s
TI 83/84 Statistics Summary – Formulas
Factorial
k! = k. (k-1). (k-2)…. 3. 2. 1
Binomial Coefficient
( nx ) =
Where:
n!
x!(n-x)!
x is the number of successes
(between 0 & n)
n is the number of trials
(n – x) is the number of failures
Binomial Probability Formula
P(X = x) =
( nx ) p
Where:
x
(1-p)n-x
P(X=x) is the probability of x
successes
x is the number of successes
(between 0 & n)
n is the number of trials
(n – x) is the number of failures
p is the probability of success
of a single trial
(1 – p) is the probability of
failure of a single trial
Studentized Version of Sample Means
(t-Score)
t=
x–m
s/ n
Where:
x is the sample mean
m is the population
mean
s is the sample
standard
deviation
n is the sample size
df (degrees of freedom)
=n-1
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