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Statistics

What is Statistics?
What is statistical mean, median, mode, and range?
What are my hypotheses?
What is a p-value, really?
How do I know what analysis to do?

What is Statistics?
Statistics is the study of the collection, organization, analysis, interpretation and presentation of data.

What is statistical mean, median, mode, and range?
Calculating the Mean, Median, Mode and Range for simple data
The table below shows how to calculate the mean, median, mode and range for two sets of data.
Set A contains the numbers 2, 2, 3, 5, 5, 7, 8 and Set B contains the numbers 2, 3, 3, 4, 6, 7.

Measure Set A
2, 2, 3, 5, 5, 7, 8 Set B
2, 3, 3, 4, 6, 7

The Mean
To find the mean, you
need to add up all the
data, and then divide
this total by the number
of values in the data.
Adding the numbers up gives:
2 + 2 + 3 + 5 + 5 + 7 + 8 = 32
There are 7 values, so you divide
the total by 7:    32 ÷ 7 = 4.57...
So the mean is 4.57 (2 d.p.)
Adding the numbers up gives:
2 + 3 + 3 + 4 + 6 + 7 = 25
There are 6 values, so you divide
the total by 6:    25 ÷ 6 = 4.166...
So the mean is 4.17 (2 d.p.)

The Median
To find the median, you
need to put the values
in order, then find the
middle value. If there are
two values in the middle
then you find the mean
of these two values.
The numbers in order:
2 , 2 , 3 , (5) , 5 , 7 , 8
The middle value is marked in
brackets, and it is 5.

So the median is 5
The numbers in order:
2 , 3 , (3 , 4) , 6 , 7
This time there are two values in
the middle. They have been put
in brackets. The median is found
by calculating the mean of these
two values:    (3 + 4) ÷ 2 = 3.5
So the median is 3.5

The Mode
The mode is the value
which appears the most
often in the data. It is
possible to have more
than one mode if there
is more than one value
which appears the most. The data values:
2 , 2 , 3 , 5 , 5 , 7 , 8
The values which appear most
often are 2 and 5. They both
appear more time than any
of the other data values.

So the modes are 2 and 5
The data values:
2 , 3 , 3 , 4 , 6 , 7
This time there is only one value
which appears most often - the
number 3. It appears more times
than any of the other data values.

So the mode is 3

The Range
To find the range, you
first need to find the
lowest and highest values
in the data. The range is
found by subtracting the
lowest value from the
highest value. The data values:
2 , 2 , 3 , 5 , 5 , 7 , 8
The lowest value is 2 and the
highest value is 8. Subtracting
the lowest from the highest
gives:    8 - 2 = 6
So the range is 6
The data values:
2 , 3 , 3 , 4 , 6 , 7
The lowest value is 2 and the
highest value is 7. Subtracting
the lowest from the highest
gives:    7 - 2 = 5
So the range is 5

1.Introduction
2.Different Types of Data

3.Methods of Data Collection
4.Data Analysis
5.Summary Statistics
6.Displaying Data

7.Probability
8.Distributions
9.Testing Statistical Hypothesis
10.Point Estimates
11.Practice Problems
12.Numerical Methods
13.Multivariate Data Analysis
14.Analysis of Specific Datasets

Analysis of Variance
Confidence Intervals
Calculation of Normal Probabilities
Correlation and Regression Analysis
Create scatter plots
Create Time Series plots
Descriptive Statistics
Hypothesis Testing
Linear Regression Tool
Mean & St. Dev. Calculator
Metric Conversions
Normal Probability Tool
Pie Chart Tool
Quadratic Equations Solver
Solved Statistics Problems
System of Equations Solver

What conclusions can be drawn from sample data?
What is the degree of certainty of these conclusions?
What actions should be taken on the basis of the conclusions drawn from these data?