Transcript S DEVIATION

S D.
• In probability and statistics, the standard
deviation is the most common measure of
statistical dispersion. Simply put, standard
deviation measures how spread out the values
in a data set are.
• More precisely, it is a measure of the average
distance of the data values from their mean. If
the data points are all close to the mean, then
the standard deviation will be low (closer to
zero).
• If many data points are very different from the
mean, then the standard deviation is high
(further from zero). If all the data values are
equal, then the standard deviation will be zero.
• The standard deviation is defined as the
square root of the variance.
• This means it is the root mean square
(RMS) deviation from the arithmetic mean.
The standard deviation is always a
positive number (or zero) and is always
measured in the same units as the original
data.
• For example, if the data are distance
measurements in meters, the standard
deviation will also be measured in meters.
–
• In other words, the standard deviation of a
discrete uniform random variable X can be
calculated as follows:
• For each value xi calculate the difference
between xi and the average value .
• Calculate the squares of these differences.
• Find the average of the squared
differences. This quantity is the variance
σ2.
• Take the square root of the variance.
• Example
. Our example will use the ages of four
young children: { 5, 6, 8, 9 }.
• Step 1. Calculate the mean/average :
• Step 2. Calculate the
standard deviation :
•
•
Replacing N with
4
Venn Diagram
• The Venn Diagram is made up of two or
more overlapping circles. It is often used in
mathematics to show relationships
between sets.
BAR DIAGRAM
90
80
70
60
50
40
30
East
West
North
20
10
0
1st Qtr 2nd Qtr 3rd Qtr 4th Qtr
HISTOGRAM
• The most common form of the histogram
is obtained by splitting the range of the
data into equal-sized bins (called classes).
Then for each bin, the number of points
from the data set that fall into each bin are
counted. That is
• Vertical axis: Frequency (i.e., counts for
each bin)
• Horizontal axis: Response variable
EPIDEMIC CURVE
• Depending on the information available in a
particular outbreak situation, an epi curve can provide
insight into
the pattern of disease spread, the magnitude of the
outbreak, the
time trend involved, the outlying cases, the period of
exposure
and/or the incubation period of the organism involved.
All of these pieces of information can be valuable.
For example, an epidemic
curve may allow you to see that the outbreak appears to
be from a
point source, or that it is ongoing.
Frequency polygon
• A frequency polygon is a graphical display
of a frequency table. The intervals are
shown on the X-axis and the number of
scores in each interval is represented by
the height of a point located above the
middle of the interval. The points are
connected so that together with the X-axis
they form a polygon.