Download Standard Deviation

13/14 Semester 1
Computer Programming
(TKK-2144)
Instructor: Rama Oktavian
Email: [email protected])
Office Hr.: T.12-14, Th. 12-14
Outlines
1. Statistical calculation (theory)
2. Statistical calculation (exercise)
Statistics
Statistics: Basic Ideas
 Statistics is the area of science that deals with


collection, organization, analysis, and
interpretation of data.
It also deals with methods and techniques that
can be used to draw conclusions about the
characteristics of a large number of data points-commonly called a population-By using a smaller subset of the entire data.
Statistics
Statistics in Engineering
 Engineers apply physical
and chemical laws and
mathematics to design,
develop, test, and
supervise various products
and services.
 Engineers perform tests to
learn how things behave
under stress, and at what
point they might fail.
Statistics
Statistics in Engineering
As engineers perform experiments, they collect data that can be
used to explain relationships better and to reveal information about
the quality of products and services they provide.
Statistical method
Statistics
Statistics in Chemical Engineering
Why??
Statistical methods of data analysis are valuable tools to
chemical engineers in both research and in industrial
practice.
Statistics
Statistics in Chemical Engineering
Example
- Reliable and reproducible the temperature measurements??
- Temperature variation??
- Draw a conclusion
Statistics
Basic terms in Statistics
Population
Any entire collection of people, animals, plants or things from which
we may collect data. It is the entire group we are interested in, which
we wish to describe or draw conclusions about.
Sample
A group of units selected from a larger group (the population). By
studying the sample it is hoped to draw valid conclusions about the
larger group.
Statistics
Basic terms in Statistics calculation
Mean (AVERAGE): The sum of all samples divided by the number of values
n
x
x
i
1
n
Median (MEDIAN): the middle value of a set of data containing an odd
number of values, or the average of the two middle values of a set of data
with an even number of values. For example, to find the median of {9, 3, 6,
7, 5}, we first sort the data giving {3, 5, 6, 7, 9}, then choose the middle
value 6. If the number of observations is even, e.g., {9, 3, 6, 7, 5, 2}, then
the median is the average of the two middle values from the sorted
sequence, in this case, (5 + 6) / 2 = 5.5.
Mode : The value that is observed most frequently. The mode is undefined
for sequences in which no observation is repeated.
Statistics
Methods of Variability Measurement
Variability (or dispersion) measures the amount of scatter in a dataset.
Commonly used methods: range, variance, standard deviation,
interquartile range, coefficient of variation etc.
Range: The difference between the largest and the smallest observations.
The range of 10, 5, 2, 100 is (100-2)=98. It’s a crude measure of variability.
Statistics
Methods of Variability Measurement
Standard Deviation: It gives an idea of how close the entire set of data is
to the average value. Data sets with a small standard deviation have tightly
grouped, precise data. Data sets with large standard deviations have data
spread out over a wide range of values.
s
2


x

x
 i
n 1
Sample variance (VAR): Square of the standard deviation:
n
s2 
 x
 x
2
i
1
n 1
Outliers are values xi which differ significantly from the mean
Statistics (Exercise)
How to access statistical functions in Excel 2007
Instead of using the menu, you
can type in the functions. So,
=average(b2:b16) finds the mean
of the values in cells b2 thru b16.
Statistics (Exercise)
How to access statistical functions in Excel 2007
Descriptive Statistics – “Location”
 Mean (average)
– Strongly affected by unusual points
– =average(b2:b28)
 Median (50% of data higher, 50% of data lower)
– Seldom strongly affected by unusual points
– =median(b2:b28)
Statistics (Exercise)
How to access statistical functions in Excel 2007
Descriptive Statistics – “Variability”
 Standard Deviation, =stdev(b2:b28)
– A measure of how widely the data is spread around
the mean
– Strongly affected by unusual points
 Relative Standard Deviation
– =stdev(b2:b28)/average(b2:b28)
– Usually given as percentage
 Format > Cells > Percent
 Variance
– =(stdev(b2:b28))^2
– =Var (b2:b28)
Statistics (Exercise)
How to access statistical functions in Excel 2007
Population Mean
Statistics (Exercise)
How to access statistical functions in Excel 2007
Summarizing Data
Try out the various descriptive statistics to summarize the “location” and
“variability” of the data
To summarize the data, we need more statistics power. To get more statistics
power from Excel, you need to add in the Analysis ToolPak
Statistics (Exercise)
How to access statistical functions in Excel 2007
Add in the Analysis ToolPak
Click the Microsoft Office button, then Excel Options.
Statistics (Exercise)
How to access statistical functions in Excel 2007
Add in the Analysis ToolPak
Click Add ins. In the “Manage” box, select Excel Add ins. Click “Go”
Statistics (Exercise)
Add in the Analysis ToolPak
• Click the checkbox for the Analysis ToolPak, then ‘OK’
• Install it if it isn’t installed
• When you have added it in, it will appear on the ‘Data’ page
Statistics (Exercise)
Add in the Analysis ToolPak
Optional method:
•Select Data
•Select Data Analysis
•Select Descriptive Statistics
from the next dialog box
Statistics (Exercise)
Add in the Analysis ToolPak
Statistics (Exercise)
Add in the Analysis ToolPak