Statistics is the science of collecting, organizing, presenting, analyzing, and
interpreting numerical data to assist in making more effective decisions.
Types of Statistics
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Descriptive Statistics- method of organizing, summarizing, presenting,
data in an informative way.
Inferential Statistics- A decision, estimate, prediction or generalization
about a population, based on a sample.
Population is a collection of all possible individuals, objects or measurement
of interest.
A sample is the portion, or part, of the population of interest.
Types of Variables: the data can have a qualitative or attribute variable and
quantitative variable.
Quantitative variables can be further classified as discrete variable or
continuous variable.
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Discrete variable- assume certain values where there are gaps
between values.
Continuous Variable- assume any value within a specified range.
Levels of measurement aid on how the data could be summarized and
presented and also helps to determine the type of statistical analysis that
can be performed on the data.
There are four levels of measurement of data:
1. Nominal- classified into categories but cannot be arranged in order.
2. Ordinal- data arranged in order but difference of values are
meaningless or cannot be determined.
3. Interval- similar to ordinal but difference of values have meaning that
can be determined. Moreover, there is no natural zero point.
4. Ratio- interval level with an inherent zero starting point. Differences
and ratios are meaningful for this level of measurement.
Arithmetic mean is the widely used measure of location. It requires an
interval scale. It is the only measure of central tendency where the sum of
the deviations of each value from the mean is zero.
For ungrouped data, the population mean is the sum of all the values in the
population divided by the total number of population values.
For ungrouped data, the sample mean is the sum of all the sample values
divided by the number of sample values.
The median is the midpoint of values after the data has been arranged from
the smallest to the largest.
The mode is the value of the observation that appears most frequently.
Measure of Shape
Skewness the extent of asymmetry in the distribution. If the distribution is
symmetric then it is not skewed.
Mean=Median=Mode- Symmetric
Mean>Median>Mode- Positively Skewed
Mean<Median<Mode- Negatively Skewed
Dispersion- reasons to study dispersion
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It is the measure of location of mean or median that is only describing
the center of the data.
The dispersion in a set of data helps to compare the spread of data in
two or more distributions.
Measures of Dispersion:
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Range- the largest value- smallest value