Exam 1- Ch 1, 2, 3, & 6 Flashcards
Statistics that collects, organizes, and presents the data
Descriptive Statistics
The methodology of extracting useful information from a data set
Statistics
Statistics that draws conclusions about a population based on sample data from that population
Inferential statistics
Consists of all items of interest
Population
A subset of the population
Sample
Data collected by recording a characteristic of many subjects at the same point in time, without regard to differences in time
Cross-sectional data
Data collected by recording a characteristic of a subject over several time periods
Time series data
Two types of variables
Qualitative and quantitative
This quantitative variable assumes a countable number of distinct values
Discrete
Ex: number of children, points scored in a game
Quantitative variable that can assume an infinite number of values within some interval
Continuous variable
Ex: weight, height, investment return
Scales of measure
Nominal
Ordinal
Interval
Ratio
The least sophisticated level of measurement
Data are simply categories for grouping the data
Nominal scale
Data may be categorized and ranked with respect to some characteristic or trait
Differences between categories are meaningless because the actual numbers used may be arbitrary
Ordinal scale
Data may be categorized and ranked with respect to some characteristic.
No “absolute 0”
Interval scale
Strongest level of measurement
There IS an “absolute 0”
Ratio scale
The characteristic of an observation or individual
Variable
The values associated with a variable
Data
By dividing each category’s frequency by the sample size, you get what?
Relative frequency
A segmented circle whose segments portray the relative frequencies of the categories of some qualitative variable
Pie chart
Depicts the frequency or the relative frequency for each category of the qualitative data as a bar rising vertically from the horizontal axis
Bar chart
Identifies the proportion or fraction of values that fall into each class
Relative frequency distribution
Gives the proportion or fraction of values that fall below the upper limit of each class
Cumulative relative frequency distribution
A visual representation of a frequency or a relative frequency distribution
Histogram
Shape of distribution
Typically symmetric or skewed
Shape of distribution that is a mirror image on both sides of its center
Symmetric
Shape of distribution where data forms a long, narrow tail to the right
Positively skewed
Shape of distribution where data forms a long, narrow tail to the left
Negatively skewed
A visual representation of a frequency or a relative frequency distribution
Polygon
A visual representation of a cumulative frequency or a cumulative relative frequency distribution
Ogive
Provides a visual display of quantitative data, it gives an overall picture of the data’s center and variability
Stem and leaf diagram
The primary measure of central location
Arithmetic mean
Another measure of central location that is not affected by outliers
Median
Another measure of central location, by the most frequently occurring value in a data set
Mode
Measures of dispersion include:
Range
Mean Absolute Deviation
Variance and Standard Deviation
Coefficient of Variation
? = maximum value - minimum value
? = range
An average of the absolute difference of each observation from the mean
Mean absolute deviation (MAD)
This adjusts for differences in the magnitudes of the means
Coefficient of variation
The manner in which data are distributed
Shape
A measure of symmetry of the lack of it
Soreness
A measure of whether data are peaked of flat relative to a normal distribution
Kurtosis
For any data set, the proportion of observations that lie within k standard deviations from the mean is at least 1-1/k^2, where k is any number greater than 1
Chebyshev’s Theorem
Empirical Rule
Empirical Rule
Describes the likelihood that x assumes a value within a given interval
Probability density function
For any value x of the random variable X, the cumulative distribution function f(x) is computed as f(x) = P(X _< x)
Cumulative density function
Describes a random variable that has an equally likely chance of assuming a value within a specified range
Continuous uniform distribution
Closely approximates the probability distribution of a wide range of random variables
Normal distribution
Characteristics of normal distribution
Symmetric- about its mean
Asymptotic- that is, the tails get closer and closer to the horizontal axis, but never touch it
Normal distribution is completely described by two parameters
u is the population mean which describes the central location of the distribution
o^2 is the population variance which describes the dispersion of the distribution
A special case of the normal distribution
Standard normal (z) distribution
Gives the cumulative probabilities P(Z _< z) for positive and negative values of z
Standard normal table (Z table)
