Need More Information?
The following websites provide information on how to reduce the carbon emissions and
costs associated with construction site energy use:
The Strategic Forum for Construction has produced an action plan for reducing CO2 emissions
on
Variance and standard deviation (grouped data)
Introduction
In this leaet we extend the denitions of variance and standard deviation to data which has been
grouped.
Variance
The variance of a set of values, which we denote by 2 , is dened as
f (x x)2
n
wh
Measures of Location
Averages
Averages can be tricky.
Consider:
Rate of
Return
Year 1
Year 2
Year 3
Year 4
Year 5
0.07
0.1
0.12
0.3
0.15
What is the average rate of return over the five year period?
Arithmetic average = .148
Correct average = .145321
Cons
Statistics - Median of Grouped Data
On arranging the data in ascending or descending order median is the middle - most
observation. If the number of observations are odd then the median is (n+1 / 2)th
observation where 'n' is the number of observations. I
Chapter 3 Descriptive Statistics: Numerical Measures
Slide 1
Learning objectives
1. Single variable Part I (Basic) 1.1. How to calculate and use the measures of location 1.2. How to calculate and use the measures of variability 2. Single variable Part II
Including Revision 1 dated May 2012
Including Revision 1 dated May 2012
Page 4
2009 Edition - Revision 1
Standard:
07
Signs and other devices that do not have any traffic control purpose that are placed within the highway
right-of-way shall not be locat
D. Cvitanic, I. Lozic, D. Breski: An analysis of intersection traffic signal warrants
DRAZEN CVITANIC, M. Se.
e-mail address: Drazen.Cvitanic@gradst.hr
IVO LOZIC, D. Se.
DEANA BRESKI, B. Eng.
Sveuciliste u Splitu
Gradevinsk.i fakultet
Matice hrvatske 15,
Ordinary Dierential Equations
1
Introduction
A dierential equation is an equation relating an independent variable, e.g. t, a dependent variable, y,
and one or more derivatives of y with respect to t:
dx
= 3x
dt
y2
d2 y
dy
= 0.
+ 3x2 y 2
dx2
dx
dy
= et
dt
Differentiation Rules Calculus I
General Formulas 1. 2. 3. 4. 5.
d dx k
Integration Formulas Calculus I
General Formulas 1. k dx = kx + C. (u + v) dx = (u - v) dx = u dv = uv - u dx + u dx - v dx. v dx.
= 0. + v) = - v) =
du dx du dx
d dx (u d dx (u
+ -
d
CALIBRATING FREEWAY SIMULATION
MODELS IN VISSIM
Submitted By:
Tony Woody
Master of Science in Civil Engineering
CEE 600 Final Research Report
University of Washington
Seattle, WA
Spring Term 2006
Abstract
The microscopic traffic simulation software progra
Formulas from Calculus
Derivatives
d
dx
d
dx
d
dx
[xn ]
= nxn1
[c]
=0
[x]
d
dx
d
dx
d
dx
[ x]
d
dx
1
x
[ex ]
= ex
[bx ]
= bx ln b
=1
d
dx
d
dx
d
dx
[ln x]
=
1
x
1
= x2
d
dx
[logb x]
=
1
x2
2
= x3
d
dx
d
dx
[sinh x]
= cosh x
[cosh x]
= sinh x
d
dx
d
dx
d
d
Christen G. Byler
Christen G. Byler is an economist
in the Division of Census of Fatal
Occupational Injuries, Ofce
of Compensation and Working
Conditions, Bureau of Labor
Statistics. Email: byler.christen@
bls.gov.
Hispanic/Latino fatal
occupational injur
Owner Controlled Insurance Programs - Part 1
David L. Grenier
Owner-controlled insurance programs (OCIPs) are a type of wrap-up, an increasingly popular insurance
procurement option that allows coverages for multiple insureds to be bundled (or wrapped up)
Remediation is considered as the management of the
contaminant at a site so as to prevent, minimize or
mitigate damage to human health, property or the
environment. It is a broader term than clean up in that
remediation options can include physical action
A RATIONAL APPROACH TO THE PREDICTION OF REFLECTIVE CRACKING
IN BITUMINOUS OVERLAYS FOR CONCRETE PAVEMENTS
by
THOMAS A. BENNERT
A Dissertation submitted to the
Graduate School-New Brunswick
Rutgers, The State University of New Jersey
in partial fulfillmen
SECTION R8A
BITUMINOUS PRIME COAT
R8A 01 SCOPE
The work covered by this Section of the Specification consists in furnishing all plant, labor, equipment
and materials and in performing all operations in connection with the application of a bituminous prime
Lecture 2 Grouped Data
Calculation
Mean, Median and Mode
2. First Quantile, third Quantile and
Interquantile Range.
1.
Mean Grouped Data
Example: The following table gives the frequency distribution of the number
of orders received each day during the pas
Bed 16
Bed 10
Bed 9
Bed 17
Bed 13
Bed 12
Bed 8
Batch
Plant
Bed19
Product Storage
Bed 23
Bed 22
Bed 20
Bed 21
Bed 15
Bed 14
Bed 11
G
Finsihing Bay
D
A
Bed 18
H
E
Stock
room
Food
F
Bed 7
Bed 5
Bed 4
Bed 3
Bed 2
Bed 1
C
B
Weld
Shop
Mainte
-nance
Bed 6
Entera
MasterFlow 622
Heavy duty epoxy resin grout
DESCRIPTION
Masterflow 622 is a solvent-free rapid hardening,
high strength grout, based on modified epoxy resin
and is designed for use as a precision, heavy duty
chocking grout for engineering applications. It
WireSolutions
Prestressed concrete
Wire and strands
We are now
moving beyond
what the world
expects of steel.
WireSolutions
Build, Move & Energize!
With three factories dedicated
to prestressing wire and strands,
WireSolutions is certified in more than 20