Median
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Transcript of Median
MedianDefinition: Middle value in ordered list
• Arrange the data in increasing order
• 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
n is mean
p is prob. of success
Where: means sum (add)
is the sample mean
xi is each of the observed values
N is the sample size (number of observations)
is the Population Standard Deviation
TI 83/84 Statistics Summary – FormulasSample Mean
x =xi
n
Formula ModeDefinition: Most frequent value(s)
Where: means sum (add)
x is the sample mean
xi is each of the observed values
n is the sample size (number of observations) xi
2 – (xi)2/n
n - 1
Sample Standard DeviationFormula
s = (xi – x)2
n - 1
or
s =
(computational formula)
Where: means sum (add)
x is the sample mean
xi is each of the observed values
n is the sample size (number of observations)
s is the Sample Standard Deviation
RVCC rme Page 1
Population Mean
=xi
N
FormulaWhere: means sum (add)
is the sample mean
xi is each of the observed values
N is the population size (number of observations)
Population Standard DeviationFormula
= (xi – )2
N
or
(computational formula)
= xi
2
N– 2 Definition: IQR = Q3 – Q1
RangeDefinition: Range = Max - Min
QuartilesDefinition: 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
• 2nd Quartile – Median of the original data set
• 3rd Quartile – Throw away all values below the median. 3rd Quartile is the median of the remaining data
Definition: Min, Q1, Q2, Q3, Max
Formula
Lower and Upper Limits
Definition: Lower Limit = Q1 – 1.5 * IQR
Upper Limit = Q3 + 1.5 * IQROutliersDefinition: Data values below the lower limit or above the upper limit
z-Score (standard score)Meaning: z-Score tells the number of standard deviations an observed value is from the mean
z =x –
z =
x – x
s
Five-Number Summary
Interquartile Range (IQR)
Mean of a Discrete Random VariableFormula: = xP(X=x)
Mean of a Binomial Random VariableFormula: = np
Where: x is each of the observed values
P(X=x) is the probability of the observed value
Where: n is the number of trials (outcomes)
p is the probability of success
Mean of a Discrete Random Variable
Where: x is each of the observed values
P(X=x) is the probability of the observed value
is the mean
Formula: = x – P(X=x)
Formula: = xP(X=x) – 2
or
(Computational formula)
Std. Dev. of a Binomial Random VariableFormula: = np(1-p)
TI 83/84 Statistics Summary – Formulas RVCC rme Page 2
Binomial Probability Formula
P(X = x) = ( ) px (1-p)n-xnx
Where: 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
Binomial Coefficient
( ) = n n! x x!(n-x)!
Where: x is the number of successes (between 0 & n)
n is the number of trials
(n – x) is the number of failures
Factorial
k! = k. (k-1). (k-2)…. 3. 2. 1
Studentized Version of Sample Means (t-Score)
x – s/ n
t =Where: x is the sample mean
is the population mean
s is the sample standard deviation
n is the sample size df (degrees of freedom)
= n - 1