BIOL 110 1st Edition Lecture 4 Outline of Last Lecture I Traverse computations and map making sections 3 10 3 16 II Making a map III Closing the area IV Acceptable error V Adjusting azimuths VI Latitudes and departures VII Estimating area using Dot Grid Method VIII Estimating area using scaling triangle method Outline of Current Lecture I Measures of Central Tendency II Measures of Dispersion III Key Points Current Lecture 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 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 III 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 the spread of the center half of the data set o 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 the sample means of repeated samples taken from the sample population o 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 Key Points a 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 distribution