This document provides an overview of common statistical tools including: - The arithmetic mean, which is the sum of a list of numbers divided by the total number of items. It provides an overall trend of data. - Frequency distributions which show how many evaluations fall into various categories using tables, histograms or pie charts. - Bar graphs which present categorical and numeric variables in class intervals through bars to show patterns. - Standard deviation which measures how spread out numbers are from the mean. A low standard deviation means numbers align with the mean. - T-tests and Pearson's correlation coefficient which measure relationships between variables, and the chi-square test which compares expected to observed categorical variable frequencies.

1. Common
Statistical Tools
Presented by: Daian P. Moreno
Victorias National High School
Victorias City, Negros Occidental

2. Arithmetic Mean
• The arithmetic mean, more commonly known as “the
average,” is the sum of a list of numbers divided by the
number of items on the list.
• The mean is useful in determining the overall trend of a
data or providing a rapid snapshot of your data.
• Another advantage of the mean is that it’s very easy and
quick to calculate.

3. Arithmetic Mean
• The arithmetic mean allows investors to gain some
insight into stock prices, economic data, and a host of
other information.
• For instance, if Company XYZ's stock price is trading
above its arithmetic mean, it could be that the stock is
overvalued.

4. Frequency Distribution
• Is presented in tables or charts that show how many of
your evaluation participants fall into various categories of
interest (Wilder Research, 2009).
• A graph or data set organized to show the frequency of
occurrence of each possible outcome of a repeatable
event observed many times.
• A frequency distribution can be graphed as a histogram or
pie chart.

5. Pie Chart
• A pie graph (or pie chart) is a specialized graph used in statistics.
• Represents the percentage of that category.

6. Bar Graph
• Bar graph may be either horizontal or vertical.
• Bar graphs are one of the many techniques used to
present data in a visual form so that the reader may
readily recognize patterns or trends.
• Bar graphs usually present categorical and
numeric variables grouped in class intervals.
• Is equal to the frequency (number of observations) in
the category. Leave space in between the bars to
emphasize that there is no ordering in classes.

7. Example of a Bar Graph

8. Standard Deviation
• Often represented with the Greek letter sigma (σ),
is the measure of a spread of data around the
mean.
• A high standard deviation signifies that data is
spread more widely from the mean, where a low
standard deviation signals that more data align with
the mean.

9. T-Tests
• Are used to test if the difference of means is
statistically significant. It test if the sample is
representative of populations.
• For example, if the mean for variable 1 is 40
and the mean for variable 2 is 56, you may
say the means are different.

10. Pearson’s Correlation Coefficient (r)
• Pearson’s correlation coefficient is the test statistics that
measures the statistical relationship, or association,
between two continuous variables.
• It is known as the best method of measuring the
association between variables of interest because it is
based on the method of covariance.
• It gives information about the magnitude of the
association, or correlation, as well as the direction of the
relationship.

11. Chi-square Test
• The Chi Square statistic is commonly used for testing
relationships between categorical variables. Compares the
frequency count of what is expected in theory against what is
actually observed.
• The null hypothesis of the Chi-Square test is that no relationship
exists on the categorical variables in the population; they are
independent.
• An example research question that could be answered using a
Chi-Square analysis would be: Is there a significant relationship
between voter intent and political party membership?

12. References
• https://investinganswers.com/financial-dictionary/ratio-
analysis/arithmetic-mean-2546
• https://www.britannica.com/technology/frequency-distribution
• https://whatis.techtarget.com/definition/pie-graph-or-pie-chart
• https://www.statcan.gc.ca/edu/power-pouvoir/ch9/bargraph-
diagrammeabarres/5214818-eng.htm
• http://www.statisticssolutions.com/pearsons-correlation-
coefficient/
• http://www.statisticssolutions.com/using-chi-square-statistic-in-
research/