Statistics
Skewed
non symmetrical, the values of the mean, median, and mode change.
Mutually Exclusive
one variable cannot belong to more than one class
Samples
portion, or part, of the population of interest. Samples are often used to obtain reliable estimates of population parameters.
Quantitative
a variable can be reported numerically
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.
Population
The entire set of individuals or objects of interest or the measurements obtained from all individuals or objects of interests.
Attribute or Qualitative
When an object or individual is observed and recorded as a nonnumeric characteristic., count the number of observation for each category
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.
Frequency Table
a grouping of qualitative data into mutually exclusive and collectively exhaustive classes showing the number of observations in each class.
Raw data
are data that have not been grouped in a frequency distribution.
Discrete variable
assume only certain values. There are gaps between values Discrete variables are counted
Collectively exhaustive
every variable is accounted for
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.
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 of the mean is at least 1-1/k^2, where k is any value greater than 1.
Nominal Level of measurement
It is the lowest measurement It has no particular Order. It can only be classified and count.
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, such as gross domestic product, which compound or build on each other
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.
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.
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.
Arithmetic mean
• Most widely used • Widely reported measure of location. • We study the mean as both population parameter and a sample statistic.
Frequency Distribution
A grouping of quantitative data into mutually exclusive and collectively exhaustive classes showing the number of observation in each class. pg 27
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. (¯X+3S and ¯X-3s). At least 24 of 25 values, or 96% will lie between + and - 5 standard deviation of the mean. (¯X+5s and ¯X-5s)
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 deviations of the mean.( ¯X+2s and ¯X-2s) 99.7% will lie within plus and minus 3 standard deviations of the mean (¯X+3s and ¯X-3s)
Descriptive Statistics
Methods of organizing, summarizing, and presenting data in an informative way.
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.
Ordinal Level Data
Ranked Rated on a relative scales the difference is not known. Count Number of observation divide the total number of observation.
What is statistics?
Statistics is a set of knowledge and skills used to organize, summarize and analyze data
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)
Inferential Statistics
The method used to estimate a property of a population on the basis 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.
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 measure of dispersion indicates that the mean is not reliable. The second reason for studying the dispersion in a set of data is to compare the spread in two or more distributions.
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
Bimodal
having two modes
