Chapter 1-4 Statistics Frequency Distribution And Population
In this chapter we discuss statistics frequency distribution and population.
Population
the entire collection of individuals or objects about which information is desired. may be considered to be finite or infinite
Census
a collection of data from every member of the population
Sample
a sub-collection or subset of a population selected for study
a numerical characteristic of a population
Statistic
a numerical characteristic of a sample
the characteristic about which we are interested
Data
the observations that have been collected
Qualitative Data
categorical or attribute data
Quantitative Data
numerical data
Discrete Data
count dataquantitative)
Continuous Data
measure dataquantitative)
Sampling Error
the difference between the result of a sample and the result for the entire population. caused by random fluctuations of the sample- i.e. by chance
Normal
bell-shaped distribution
Statistically Significant
observation that is extremely unlikely to happen simply by chance
Descriptive Statistics
the collection, presentation, and description of data
Inferential Statistics
interpreting the data in order to draw conclusions about the population, based on information obtained from a sample
Frequency Distribution
a chart or table giving the values of a variable together with their corresponding frequencies
Blood Type
example of a frequency distribution for qualitative data
Class Width
the difference between two consecutive lower class boundaries
Class Midpoints
the center value of each class
Relative Frequency
a proportional measure of frequency, calculated by dividing the frequency of that class by the total frequency of the data set
Pie Chart
a circular graph showing the relationships of parts to a whole, only one variable at a time may be displayed
Bar Graph
a rectangular graph representing quantities using heights of detached rectangles, generally used to display qualitative or discrete data, displays an ungrouped frequency distribution
Histogram
a rectangular graph representing quantities using heights of attached rectangles, used to display continuous data, displays a grouped frequency
Elements of a Histogram
a title, a horizontal scaleidentifying the variable), a vertical scaleidentifying frequencies)
Stem and Leaf Display
combines graphing and sorting the data, split into the leading digits, the trailing digits
Outlier
an unusually large or small data value with respect to its data set
Dotplot
a number line above which each data value is plotted as a point
Measures of Central Tendency
the middle or center of a data set, averages- mean, median, mode, midrange
Averages
mean, median, mode, midrange
Arithmetic Mean
adding the data values and dividing by the number of data values, balance point of a data set
X Bar
sample mean – statistic
Mu
population mean – parameter
Median
physical center of a data set
Mode
the most frequently occurring value in a data set
Bimodal
when two values occur with the same greatest frequency
Midrange
the value midway between the lowest and highest values in a data set, L+H/2
Measures of Dispersion
measure the spread or variability of the data set
Range
the difference between the largest and smallest values in a data set
Standard Deviation
the average distance of the data values from their mean
Within 1 Standard Deviation
68%
Within 2 Standard Deviations
95%
Within 3 Standard Deviations
99.7%
Measures of Relative Standing
indicates the position of a data value in terms of its data set
Z-Score
gives the position of a data value in terms of standard deviations from its mean
Quartiles
divide an ordered data set into four equal parts
Five-Number Summary
Lowmin), Q1, medianQ2), Q3, and highmax)
Interquartile Range
Q3-Q1
Probability
______ that an event will occur is the relative frequency with which that event can be expected to occur
P
theoretical probability
P’
empirical probability
Sample Space
the set of all possible outcomes of an experiment
Sample Points
the individual outcomes in a sample space
Event
any subset of a sample space
A Complement
the set of all sample points in the sample space that do not belong to A
Compound Event
any event made up of two or more sample events
P(A or B)
probability that either A or B occurs
Mutually Exclusive
events cannot happen at the same time
General Addition Rule
P(A or B) = P(A) + P(B) – P(A and B)