Input calculations "freely" in the text area below and
activate by the click or moving to outside of the input area.
Max. one calculation for each row, you can divide
an equation in multiple lines by ( ). Separate
distinct elements in the same row with ; character but do not end
the row with ; character.
Blank rows are ignored.
The calculator "exploits"
math.js
Javascript library.
The answers (A1,A2,...) of the calculations are
printed in the output box.
Let's learn a bit how to analyze different kinds of statistical data.
This page will contain material that might be useful for you
when you want to get more control of the statistical information
and the methods shaping the data (statistics, cost calculations,...).
What is statistics? (hover on me)
Statistics is about learning from data, making useful
models "of the world". To describe, analyse, post-shape, correlate,
predict, simulate, to make causal inferences, ...
of the phenomenom in question. Getting control over the things
(with the help of the data).
Data you have is often only a partial "image" of the real world,
you also need good (theory, common sence,...)
concepts "above" it and understand e.g. how much
subjectivity/objectivity influences how the real data is generated.
Remember also that statistics is not just about the numbers,
you can also analyse e.g. written text by
certain statistical methods.
Description of the simple set of numbers
Let's generate a set of numbers which
we call variable or data "x" (variable could be e.g. monthly wage) .
Summary statistics (the above variable x):
.
"The Extremist" measure: ?
What is the cumulative probability? (hover on me)
Cumulative probability
tells how much probability or relative frequency
mass is cumulated below the certain value of the
statistical variable (x). In the above graph variable x goes
along the horizontal axis and the corresponding cumulative
probability values are on the vertical axis. X-numbers are
ordered from the lowest value to the highest (the horizontal axis) and
probability "grows" from 0 to 100 (%) without descending in any point.
In the graph you can "easily" see the percentile points (e.g.
50 % = median point).
Cumulative values may not be as intuitive as
its "histogram" or "bar diagram" counterpart but it is
one way to look at the distribution of the variable x and
via it the theoretical distribution of x (e.g. normal) is
determined.
What is bar diagram? (hover on me)
Relative differences and changes
Relative difference between two numbers
Logarthmic difference or change is useful in certain situations,
it is close to the traditional relative change when
the change is small.
Weighting observations
Weighted average
Weigted average of variable x means that it values
are weighted in a certain way. Calculating the weighted average
you will need another variable called weight-variable w.
w-variable can have zero or greater values (>=0).
x and w variables must equal in their lengths (number of observations).
x (variable) w (weighting):
Result: weighted average (mean) of x (by w) =
.
How to calculate weighted average? (hover on me)
In the normal (arithmetic) average
each x-value is weighted by the same number 1. E.g.
the normal average of 2 and 3 = (1*2 + 1*3)/(1+1) = (2+3)/2 = 2.5.
With weights symbols (w1*2 + w2*3)/(w1+w2).
So weights of the numbers are w1 = w2 = 1 . In the case of
the weighted average
the weights w1,w2,... can be different - or same :).
You can conclude that weighted average is more general than "simple" average.
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