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Statistics
Chapter 3 Definitions
34
Mathematics
Undergraduate 2
03/16/2009

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Term
Descriptive Statistics
Definition
summarize or describe the important characteristics of a known set of data
Term
Inferential Statistics
Definition
use sample data to make inferences (or generalizations) about a population
Term
Measure of center
Definition
the value at the center or middle of a data set
Term
Arithmetic Mean
(Mean)
Definition
the measure of center obtained by adding    the values and dividing the total by the number of values
Term
 ∑
Definition
denotes the sum of a set of values
Term
x
Definition
is the variable usually used to represent the     individual data values
Term
n
Definition
represents the number of values in a sample
Term
N
Definition
represents the number of values in a population
Term

 

   

 x 

Definition
is pronounced ‘x-bar’ and denotes the mean of a set of sample values
Term

µ

 

 

Definition
is pronounced ‘mu’ and denotes the mean of all values in a population
Term
Median
Definition
the middle value when the original data values are arranged in order of increasing (or decreasing) magnitude
Term
Mode
Definition

the value that occurs most frequently

 

 the only measure of central tendency that can be used with nominal data 

Term
Midrange
Definition

the  value midway between the maximum and minimum values in the original data set

 

max value + min value 

Term
Round-off Rule for
Measures of Center
Definition
Carry one more decimal place than is present in the original set of values.
Term
Symmetric
Definition
Data is symmetric if the left half of its histogram is roughly a mirror image of its right half.
Term
Skewed
Definition
Data is skewed if it is not symmetric and if it extends more to one side than the other.
Term
Range
Definition

the difference between the maximum value and the minimum value of a given set of data

 

(max. value) - (min. value) 

Term
Standard Deviation
Definition
a measure of variation of values about the mean in a given set of sample values
Term
Variance
Definition
a measure of variation equal to the square of the standard deviation in a given set of values.
Term
What's the symbol for a Sample Variance?
Definition

s2

 

which is the square of the standard deviation, s

Term
What's the symbol for Population Variance?
Definition

σ2

 

which is the square of the population standard deviation, σ.

Term
What's the formula for Estimation of Standard Deviation Range?
Definition

s= standard deviation

range = (max. value) - (min. value)

 

s ≈  Range

    4
 

Term
z  Score
Definition
the number of standard deviations that a given value x is above or below the mean
Term
Whenever a value is less than the mean, its corresponding z score is positive or negative?
Definition
negative
Term
What is Q1  
Definition

(First Quartile)

separates the bottom 25% of sorted values from the top 75%.

Term
What is Q2
Definition

(Second Quartile)

same as the median; separates the bottom 50% of sorted values from the top 50%.

Term
What is Q3
Definition

(Third Quartile)

separates the bottom 75% of sorted values from the top 25%.

Term

There are how many quartiles seperating data into four parts?

 

Similarly, there are how many percentiles seperating data into 100 groups? 

Definition

3 Quartiles into 4 parts

 

99 percentiles (P1-99 ) into 100 groups

Term
What does EDA stand for?
Definition
Exploratory Data Analysis
Term
What is the EDA?
Definition
the process of  using statistical tools (such as graphs, measures of center, and measures of variation) to investigate data sets in order to understand their important characteristics
Term
Outlier
Definition
 a value that is located very far away from almost all of the other values.
Term
What is included in the 5-number summary?
Definition

the minimum value

 the first quartile Q1

 the median (or second quartile Q2)

 the third quartile, Q3

 and the maximum value

Term
Boxplot
Definition
graph of a data set that consists of a line extending from the minimum value to the maximum value, and a box with lines drawn at the first quartile, Q1; the median; and the third quartile, Q3
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