BIOL 110 1st Edition Lecture 4Outline of Last Lecture I. Traverse computations and map making (sections 3.10-3.16)II. Making a mapIII. Closing the areaIV. Acceptable errorV. Adjusting azimuthsVI. Latitudes and departuresVII. Estimating area using Dot Grid MethodVIII. Estimating area using scaling triangle methodOutline of Current Lecture I. Measures of Central TendencyII. Measures of DispersionIII. Key Points Current LectureI. 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 These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.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 points are smaller than this value (and 75% are larger) Observation to use= (n+1)/2o 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): the spread of the center half of the data seto Useful to identify outliers and to build box plots IQR= Q3-Q1- Outliers: extreme values that can cause issues in statistical results. A value may be considered an outlier if it is more than Q3 + (1.5 x IQR) or less than Q1- (1.5 x IQR)- Variance (S2): helps describes the average scatter values in a data set are around the mean; the average of the squared differences from the mean- Standard deviation (SD): helps describe the dispersion of the data around the mean; the typical or average distance a value is to the mean; the square root of the variance; an estimate of the variability of the population from which the sample was drawn- Standard Error (SE): a measure of precision/certainty in sampling results; the standard deviation of the sample means; a measure of the variability amount thesample means of repeated samples taken from the sample populationo Small SE implies that we would expect to get a similar mean estimate with repeated sampling, and a large standard SE implies that repeated sampling would result in variable mean estimates - Mean +/- SD= this is a descriptive statistic (a description of the variation) that shows how the observations within the sample differ from the sample mean. - Mean +/- SE= this is a descriptive of the bound on the estimates of the population mean/how likely the sample mean is the population mean (a probability statement)III. Key Pointsa. One plot average (sample) would not be a good estimate of the population, so we replicate b. A sample distribution allows us to see the dispersion of data (variance/SD)c. As the sample size, n, gets larger, the sample means tend to follow a normal probability