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