# Formula Review

### 2.2Measures of the Location of the Data

$i=( k 100 )( n+1 ) i=( k 100 )( n+1 )$

where i = the ranking or position of a data value,

k = the kth percentile,

n = total number of data.

Expression for finding the percentile of a data value: (100)

where x = the number of values counting from the bottom of the data list up to but not including the data value for which you want to find the percentile,

y = the number of data values equal to the data value for which you want to find the percentile,

n = total number of data

### 2.3Measures of the Center of the Data

$μ= ∑ fm ∑ f μ= ∑ fm ∑ f$ Where f = interval frequencies and m = interval midpoints.

The arithmetic mean for a sample (denoted by $x¯x$) is

The arithmetic mean for a population (denoted by μ) is

### 2.5Geometric Mean

The Geometric Mean: $x~ = (∏i=1nxi) 1n = x1·x2···xn n = (x1·x2···xn)1n x~= (∏i=1nxi) 1n=x1·x2···xn n =(x1·x2···xn)1n$

### 2.6Skewness and the Mean, Median, and Mode

Formula for skewness: $a3=∑(xi−x¯)3ns3a3=∑(xi−x¯)3ns3$
Formula for Coefficient of Variation:$CV=sx¯·100conditioned uponx¯≠0CV=sx¯·100conditioned uponx¯≠0$

### 2.7Measures of the Spread of the Data

$s x= ∑ fm2 n − x – 2 s x= ∑ fm2 n − x – 2$ where

Formulas for Sample Standard Deviation $s= Σ (x − x – ) 2 n−1 s= Σ (x − x – ) 2 n−1$ or $s= Σf (x− x – ) 2 n−1 s= Σf (x− x – ) 2 n−1$ or $s=(∑i=1nx2)-nx–2n-1s=(∑i=1nx2)-nx–2n-1$ For the sample standard deviation, the denominator is n - 1, that is the sample size - 1.

Formulas for Population Standard Deviation or or $σ=∑i=1Nxi2N-μ2σ=∑i=1Nxi2N-μ2$ For the population standard deviation, the denominator is N, the number of items in the population.