Rick F Guyon - Measures of Central Tendency - Richard F Guyon

Measures of Central Tendency

It is often unnecessary to present the experimental data in their entirety, either in tabular or graphical form. In such cases, the data and distribution can be represented by various parameters. One type of parameter is a measure of central tendency, Mode, median, and mean are measures of central tendency.

The mode is the observed value that occurs most frequently. The mode may vary greatly between series of observations. Therefore, its main use is a quick measure of the central value since little or no computation is required to find it. Beyond this, the usefulness of the mode is limited.

The median is the point in the distribution that partitions the total set of observations into two parts containing equal numbers of observations. It is not influenced by the extremity of scores on either side of the distribution. The median is found by counting up (from either end of the frequency distribution) until half of the observations have been accounted for.

Similar in concept tot he median are percentiles (percentile ranks) quartiles and deciles. The median could also have been called the 50th percentile observation. Similarly, the 50th percentile would be the observed value for which the cumulative frequency was 80%. The quartile and decile points on the distribution divide the observations or distribution into segments off 25% and 10%, respectively.

Rick F Guyon - Differential Equations - Application: Mixing - Richard F Guyon

A typical mixing problem involves a liquid-filled tank. The liquid may initially be pure or contain some solute. Liquid (either pure or a solution) enters the tank at a known rate. A drain may be present to remove thoroughly mixed liquid. The concentration of the solution the amount of solute at some given time is generally unknown.

Rick F Guyon - Differential Equations - Convolution Integral - Richard F Guyon

Rick F Guyon - A complex Laplace transform, F(s), will often be recognized as the product of two other transforms, F1(s) and F2(s), whose corresponding functions fi(f) and f2(t) are known. Unfortunately, Laplace transforms cannot be computed with ordinary multiplication. However, it is possible to extract f(t) from the convolution, as calculated from either of the convolution integrals.

Rick F Guyon - Convolution Integral - Richard F Guyon 

Rick F Guyon - Analysis of Accident Data - Richard F Guyon

Rick F Guyon - Accident data are compiled and evaluated to identify hazardous features and locations, set priorities for safety improvements, support economic analysis, and identify patterns, causes and possible countermeasures.

Accidents are classified into three severity categories,  depending on whether there is (a) property damage only referred to as PDO accidents, (b) personal injury, or (c) fatalities. The severity ratio is defined as the ratio of the number of injury and fatal accidents divided by the total number of all accidents (including PDO accidents).

It is common to prioritize intersections according to the accident rate, R. The accident rate may be determined for PDO, personal injury, and fatal accidents or the total thereof. The accident ratio is the ration of the number of accidents per year to the average daily traffic, ADT. The rate is reported as RMEV.

Rick F Guyon - Vehicle Exposure - Richard F Guyon

Routes between points are prioritized according to the accident rate per miles, calculated as the ratio of the number of accidents per year to the ADT per mile of length, counting traffic from all directions in the intersection. For convinces, the rate may be calculated per 100 million vehicle miles.

Rick F Guyon - Speed Degredation on Uphill Grades - Richard F Guyon

Rick F Guyon - Most modern passenger cars traveling on highways are capable of negotiation uphill grades of 4 to 5% without speed decreases blow their initial level-highway sppeds. (Older cars with high mass-to-power ratios and some smaller-sized "economy" vehicles may experience speed decreases.)

Heavy trucks experience greater speed degradation than passenger cars. The primary variables affecting actual speed decreases are the grade steepness, the grade length,  and the truck's mass-to-power ration. Mass to power ratios are commonly stated in pounds per horsepower and kilograms per kilowatt.

Rick F Guyon - Stopping Distance - Richard F Guyon

Rick F Guyon - Stopping distance includes the distance traveled before the brakes are applied as well as the distance during the breaking manuever. The breaking perception reaction time is also referred to as the PIEV time, using an acronym for perception, identification, emotion, and volition. PIEV time varies widely from person to person. Though the median value is approximately 0.90 sec for unexpected events, individuals with slow reaction times may require up to 2.7 seconds. 2.5 seconds is the value used by AASHTO for determining the minimum stopping sight distances, the value that is appropriate for approximately 90% for the population.

Rick F Guyon - Refresher: Systems of Units - Dimensional Analysis - Richard F Guyon

Dimensional Analysis

Dimensional analysis is a means of obtaining as equation that describes some phenomenon without understanding the mechanism of the phenomenon. The most serious limitation is the need to know beforehand which variables influence the phenomenon. Once these are known or assumed, dimensional analysis can be applied by a routine procedure.

The first step is to select a system of primary dimensions. The dimensional formulas and symbols for variables most frequently encountered are given .

The second step is to write a functional relationship between the dependent variable and the independent variable.

Rick F Guyon - Dimensional Analysis - Richard F Guyon