FANR 3000 1st Edition Exam 3 Study Guide Lecture 1 January 7 Population I Data Definitions a Population the set of all individuals possessing the particular attribute we wish to describe i Populations are described quantified using PARAMETERS values that summarize properties of the population ii Population mean iii Population variance 2 b Sample the portion subset of the population that we actually count or measure i Characterize a population by sampling ii Key assumption the information obtained from the sample reliably reflects the population 1 Simple random sample taking a random sample of n units from a population of size N 2 Systematic sample sampling every kth unit from a population 3 Stratified sample dividing the population into non overlapping blocks strata and taking a random sample s within strata c Variables the measurable characteristics of the samples of interest quantitative or qualitative d Observations the set of measurements we have obtained e Statistic value which summarizes a property of the sample II Types of Data a Qualitative words data observed but not really measured i Nominal no natural ordering ii Ordinal have a natural order rank b Quantitative numbers data can be measured i Discrete counts integer values only ii Continuous measurements any values within a given range Lecture 2 January 12 Precision and Accuracy I Precision and Accuracy a Accuracy the closeness of a measured value to the known true value b Precision the closeness of 2 or more measurements to each other i Independent of accuracy II III Types of error bias a Mistakes gross errors incorrect measurements due to carelessness i Reading the wrong number ect b Systematic error bias errors of the same size and magnitude with each subsequent measurement i Bent compass needle ect ii If the magnitude of error is known accuracy can be improved by a correction adjustment factor c Random error always present in a measurement i Unpredictable fluctuations in the readings due to equipment weather or reader ii Difficult to fix since errors vary in magnitude Describing and graphing data a Two primary methods of describing data i Graphically histograms bar graphs pie charts scatter plots maps ect ii Numerically means ranges variability confidence intervals ect b Histograms i Frequency quantitative qualitative 1 1 n number of observations in each variable class ii Relative frequency quantitative qualitative 1 0 1 fraction of the total observations in each variable class iii Cumulative frequency quantitative c d e f g 1 1 n the frequency of a variable class plus the frequencies of the classes below it iv Cumulative relative frequency quantitative 1 0 1 the relative frequencies plus the relative frequencies of the classes below it Ogive linear version of cumulative histograms Bar graphs associated with categories qualitative Pie chart qualitative relative frequency chart Line graph x y causation change in variable over time X Y chart not a continuous sample change in variable in relation to another Lecture 3 January 14 Making a Map I II Traverse computations and map making sections 3 10 3 16 a Take spatial information and check quality of work i Compute the sum of the interior angles sum of interior angles degrees number of sides 2 180 1 If a traverse has 5 sides ii Sum of deflection angles 360 degrees b Determining interior angles Case 1 i North not involved ii Interior angle is less than 180 degrees iii Use horizontal distance with an engineer scale iv Convert frontsights to backsights 1 Interior angle larger smaller v Deflection angle difference between 180 and the interior angle c Case 2 i North is involved ii Interior angle is less than 180 degreed 1 Ex 360 degrees 310 degrees 50 degrees 40 degrees 50 degrees 90 degrees iii Interior deflection angles 180 degrees 1 Find the direction of deflection d Case 3 i Interior angle is great than 180 degrees obtuse 1 Convert frontsight to backsight to find interior ii North is not involved iii Difference between larger and smaller angle iv Deflection negative because the sum of the interior and deflection angles about any station point must be 180 degrees Making a map a Determine scale and choose a starting point III IV V VI VII VIII b Align protractor with the paper s grid at starting point c Mark where Closing the area a Assign deflection with a direction and sign add them Acceptable error a Square root of the number of sides multiplied by the smallest angle that could be measured Adjusting azimuths a If the interior angles are less than the desired size add an equal amount to each and adjust the FS and BS accordingly b If the Latitudes and departures a Latitude the North South component of a course i Cos FS bearing x distance ii Sum should be 0 b Departure the East West component of a course i Sin ii Sum should be 0 c Use Pythagorean theorem to calculate error of closure if you don t close i Difference between latitudes and departures ii 1 total perimeter error of closure d Balancing i The correction value l sum of latitudes l x section side distance total perimeter ii Balanced departure old latitude the correction values Estimating area using Dot Grid Method Estimating area using scaling triangle method a Size area 5 base x height Lecture 4 January 21 Measurements I Measures of Central Tendency Sample Mean the average of the data set the sum of all the individual values divided by the number of observations Median the values that represents the halfway point in an ordered data set o 50 of the values are above the median 50 are below o If there is an even number of data points the median would be the average of the 2 middle values o Useful when extreme values skew the sample mean Mode the most commonly observed value in the data set II III o It s possible to have no mode in a data set or have more than one Measures of Dispersion Range the difference between the highest and lowest value in the data set Quartiles divides an ordered data set into 4 equal quarters o First quartile Q1 the median of the lower half of the data distribution 25 of the data points are smaller than this value and 75 are larger Observation to use n 1 4 o Second quartile Q2 the median of the entire data set 50 of the data points are smaller than this value and 75 are larger Observation to use n 1 2 o Third quartile Q3 the median of the upper half of the data distribution 75 of the data points are smaller than this value and 25 are larger Observation to use 3 n 1 4 Interquartile Range IQR