FANR 3000 1st EditionExam # 1 Study Guide Lectures: 1-6Lecture 1 (January 7)Population I. Data Definitionsa. Population- the set of all individuals possessing the particular attribute we wish to describei. Populations are described (quantified) using PARAMETERS: values that summarize properties of the populationii. Population mean (μ)iii. Population variance (σ2) b. Sample- the portion/subset of the population that we actually count or measurei. Characterize a population by sampling ii. Key assumption- the information obtained from the sample reliably reflects the population1. 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 population3. Stratified sample- dividing the population into non-overlapping blocks (strata) and taking a random sample(s) within stratac. 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 sampleII. Types of Data a. Qualitative: words, data observed, but not really measuredi. Nominal- no natural orderingii. Ordinal- have a natural order/ rankb. 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 AccuracyI. Precision and Accuracya. Accuracy- the closeness of a measured value to the known/ true valueb. Precision- the closeness of 2 or more measurements to each otheri. Independent of accuracyII. Types of error/biasa. Mistakes/gross errors- incorrect measurements due to carelessnessi. Reading the wrong number, ect.b. Systematic error (bias)- errors of the same size and magnitude with each subsequent measurementi. 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 measurementi. Unpredictable fluctuations in the readings (due to equipment, weather, or reader) ii. Difficult to fix since errors vary in magnitudeIII. Describing and graphing dataa. 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. Histogramsi. Frequency- quantitative/qualitative1. (1-n) number of observations in each variable class ii. Relative frequency- quantitative/ qualitative1. (0-1) fraction of the total observations in each variable classiii. Cumulative frequency- quantitative1. (1-n) the frequency of a variable class plus the frequencies of the classesbelow it iv. Cumulative relative frequency- quantitative 1. (0-1) the relative frequencies plus the relative frequencies of the classes below it c. Ogive: linear version of cumulative histogramsd. Bar graphs- associated with categories (qualitative) e. Pie chart- qualitative, relative frequency chartf. Line graph- x/y causation; change in variable over timeg. X/Y chart- not a continuous sample; change in variable in relation to another Lecture 3 (January 14)Making a Map I. 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 sidesii. 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-smallerv. Deflection angle: difference between 180 and the interior angle c. Case 2i. North is “involved” ii. Interior angle is less than 180 degreed 1. Ex. 360 degrees – 310 degrees= 50 degrees; 40 degrees + 50 degrees= 90 degreesiii. Interior + deflection angles= 180 degrees1. Find the direction of deflection d. Case 3i. 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 angleiv. Deflection: negative because the sum of the interior and deflection anglesabout any station (point) must be 180 degreesII. Making a mapa. Determine scale and choose a starting pointb. Align protractor with the paper’s grid at starting pointc. Mark where III. Closing the areaa. Assign deflection with a direction and sign; add them IV. Acceptable errora. Square root of the number of sides multiplied by the smallest angle that could bemeasuredV. Adjusting azimuthsa. If the interior angles are less than the desired size, add an equal amount to each, and adjust the FS and BS accordinglyb. If theVI. Latitudes and departures a. Latitude: the North-South component of a coursei. Cos(FS bearing) x distance ii. Sum should be 0b. Departure: the East-West component of a course i. Sin(ii. Sum should be 0c. 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. Balancingi. The correction value= l sum of latitudes l x (section (side) distance/ total perimeter)ii. Balanced departure old latitude +/- the correction values VII. Estimating area using Dot Grid MethodVIII. Estimating area using scaling triangle methoda. Size(area)= .5(base) x heightLecture 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 seto 50% of the values are above the median, 50% are belowo If there is an even number of data points, the median would be the average of the 2 middle valueso Useful when extreme values skew the sample mean- Mode: the most commonly observed value in the data set o It’s possible to have no mode in a data set or have more than one II. 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 quarterso 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)/4o Second quartile (Q2)- the median of the entire data set; 50% of the data