AEM 201 1st Edition Lecture 6PREVIOUS LECTUREI. Simultaneous Display of Multiple Variable-Two Quantitative VariablesII. Best Practices In Creating Effective Visual DisplaysIII. Numerical Methods-Measures of Location-Qualitative DataIV. Numerical Methods-Measures of Location-Quantitative DataCURRENT LECTUREI. Numerical Methods-Measures of Location-Quantitative DataII. Measures of Variability or Dispersion-Quantitative DataNUMERICAL METHODS-MEASURES OF LOCATION-QUANTITATIVE DATA- Mode: most frequently occurring value(s) in data arrayo Mo=denotation of mode for a populationo mo=denotation of mode for a sampleo To find a mode: Put data in an array and see what value(s) occurs mosto If two values occur most, the data is bimodalo If three values occur most, the data is trimodalo If four values occur most, the data is multimodalo If all data values occur with the same frequency-there is no mode (even though it could technically be considered multimodal)- Modes are very insensitive to extremes- Percentile: the pthpercentile is the value that is at least as large as p percent of all observations ina data set and is no larger than (100-p) percent of all observations in a data seto Create a data array 1sto Compute an index i-this is just the location of the number not the percentile i=(P/100)N (population) i=(p/100)n (sample)o If iis not an integer, then round up. o I i is an integer take a mean of the values in the positions i and i+1o Percentiles show where you are relative to others- Special percentiles include:o The median or 50th percentileo Deciles or 10th, 20th, 30th…100th percentilesThese 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.o Quintiles or 20th, 40th, 60th, 80th, 100th percentileso Quartiles or 25th, 50th, 75th, and 100th percentiles (known as Q1, Q2, Q3, and Q4)- Geometric Mean: the nth root of the product of n values o Computed as:  Pi tells us to multiply all of the numbers- Growth factor is what you must multiply the value of investment at the beginning of the year to find the value of investment and the end of the yearo Divide the return by 100o Add one to the resulto Multiply all growth factors and multiply by the principleo Multiply ALL together to see the return over n yearso Take the n square root to find average rate of returnover the years subtract one and thenmultiply by 100o Check to see by taking the nth root of the growth rates and take to the nth power and see if it equals the original- Rates of return are multiplicative. Compounding is the issue. Adding would be misleading because it overstates what is going ono Growth factor: change in value in period/value at beginning of period- There are many other means that we do not need to know aboutMEASURES OF VARIABILITY OR DISPERSION-QUANTITATIVE DATA- Precision and accuracy are very different- Range: absolute difference between the minimum and maximum values in a data seto Computed as: maximum value in data set-minimum value in data seto We use the smallest and largest values to compute, so the range is not very robust in respect to extremeso Doesn’t necessarily give an accurate depiction of ranges with extremes- Interquartile Range (IQR): absolute difference between the 1st and 3rd quartiles in a data set (50%trimmed range)o Computed as: Q3-Q1 or the 75th percentile-25th