Population
The entire set of individuals or objects of interest or the measurements obtained from all individuals or objects of interests.
Samples
portion, or part, of the population of interest.
Samples are often used to obtain reliable estimates of population parameters.
Inferential Statistics
The method used to estimate a property of a population on the basis of a sample.
Attribute or Qualitative
When an object or individual is observed and recorded as a nonnumeric characteristic., count the number of observation for each category
Quantitative
a variable can be reported numerically
Discrete variable
assume only certain values.
There are gaps between values
Discrete variables are counted
Continuous Variable
Observations of continuous variable can assume any value within a specific range.
Result from measuring
Example: air pressure, weight of shipment, and duration of a flight.
Nominal Level of measurement
It is the lowest measurement
It has no particular Order.
It can only be classified and count.
Ordinal Level Data
Ranked
Rated on a relative scales
the difference is not known.
Count
Number of observation divide the total number of observation.
Interval data
the next highest level of measurement.
The difference or the distance between variables is meaningful
Zero is not important.
The interval level of measurement is based on a scale with a known unit of measurement.
Frequency Table
a grouping of qualitative data into mutually exclusive and collectively exhaustive classes showing the number of observations in each class.
Mutually Exclusive
one variable cannot belong to more than one class
Collectively exhaustive
every variable is accounted for
Class Frequency
the number of observations
Relative Class Frequency
you can convert class frequencies to relative frequency to show the fraction of the total number of observation in each class.
Each class frequency/ the total number of observations.
Frequency Distribution
A grouping of quantitative data into mutually exclusive and collectively exhaustive classes showing the number of observation in each class. pg 27
Arithmetic mean
� Most widely used
� Widely reported measure of location.
� We study the mean as both population parameter and a sample statistic.
Raw data
are data that have not been grouped in a frequency distribution.
Parameter
a characteristic of a population, which is the mean value of a population.
Statistic
a characteristic of a sample, which is the mean value of a sample.
Median
The midpoint of values after they have been ordered from the minimum to the maximum values.
Mode
The mode is especially useful in summarizing nominal level data. Page 58.
It is not being affected by extremely large or low values.
Bimodal
having two modes
Skewed
non symmetrical, the values of the mean, median, and mode change.
Positively skewed distribution
The arithmetic mean is the largest of the three measures. The reason is that the mean is influenced more than the median or mode by a few extremely values. Mode<Median<Mean (skewed to the right)
Negatively Skewed
Mean<Median<Mode. The mean is influenced by a few extremely low values. Skewed to the left more. Mode is the largest value of all three measurement, the next largest measure is median and the lowest value is the Mean.
Weighted Mean
The weighted mean is a convenient way to compute the arithmetic mean when there are several observations of the same value. It helps us decide which is more valuable than the other
Geometric Mean
It is useful in finding the average change of percentages, ratios, indexes, or growth rates over time. It has a wide application in business and economics because we often interested in finding the percentage changes in sales, salaries or economic figures
Why Study Dispersion?
The reason why we study dispersion is to justify the mean. We want to know if the mean is representative or not. If the data are clustered closely around the mean. The mean is considered representative of data. However, the data are dispersed or a large m
Steps to calculate the population mean:
1. Begin finding the mean.
2. Find the difference between each observation and the mean, and square that difference.
3. Sum all the squared differences.
4. Divide the sum of the squared difference by the number of observation in the population.
Chebyshev's Theorem
It allows us to determine the minimum proportion of the values that lie within a specified number of standard deviations of the mean.
For any set of observations ( sample or population), the proportion of the values that lie within k standard deviations o
What is statistics?
Statistics is a set of knowledge and skills used to organize, summarize and analyze data
Descriptive Statistics
Methods of organizing, summarizing, and presenting data in an informative way.
Chebyshev's Theorem properties
At least 3 out of every 4,or 75%, of the values must lie between the mean + 2 standard deviation and the mean - 2 standard deviation. (�X+2S and �X-2s).
At least 8 of 9 values or 88.9%, will lie between + 3 standard deviation and - 3 standard deviation. (
The Empirical Rule Properties
For a symmetrical, bell shaped frequency distribution,
Approximately 68% of the observations will lie within plus and minus 1 standard deviation of the mean.( �X+1s and �X-1s)
About 95% of the observations will lie within plus and minus 2 standard deviati
The Empirical Rule
If a distribution is symmetrical and bell shaped, practically all of the observations lie between the mean plus and minus three standard deviations.