Chapter 6

Chapter 6

1. Distributions of Data

   • Frequency distributions are graphs that represent how often something occurs
   • Bar graphs
     • Discrete data and columns do not touch
   • Intervals are same length and both use the y-axis to represent the # of data values that fall in that interval
   • Histograms
     • Continuous data and columns do touch
   • Frequency distributions
     • Uniform distribution: equal frequencies
     • Skewed distributions: greatest frequencies is near one end
     • Mound shaped distribution: approximately symmetrical about a line passing through the interval or between the intervals with the greatest frequency
     • Bimodal distribution: two distinct intervals or groups that contain the greatest frequencies

2. Using Statistics

   • Mean: average value of data set
   • Mode: most common value
   • Median: the middle value of data arranged in increasing numerical order
   • Lower Quartile: Middle of the data that is less than the median
   • Lower extreme: The smallest value
   • Upper quartile: the middle of the data that is greater than the median
   • Upper extreme: the largest value
   • Box and Whisker Plot: a visual way of showing the minimum, lower quartile, median, upper quartile, and maximum values
   • Standard deviation:a measure of spread
     • • 1. Find mean
         • 2. Subtract each data point from the mean
           • 3. Square the difference of the data point and mean
             • 4. Find the sum of the squares and then divide by the number of data values, n
               • 5. Take the positive square root

3. Normal Distribution:

   • 68-95-99.7 rule
     • About 68% of the data are within one standard deviation of the mean
       • About 95% of the data are within two standard deviations of the mean
         • About 99.7% of the data are within three standard deviations of the mean

4. Fitting liner models to data

   • Correlation coefficient
     • "r" measures how good of a fit your regression is
       • r=1, perfectly straight and positive slope
       • r= -1, perfectly straight, negative slope
       • r=0, random scattering
   • Median-median line
     • three data points, less influenced by outliers, and y=mx+b format
     • uses summary points calculated using medians
   • Least-squares method
     • uses all data point y=mx+b format

5. Standardizing Data

   • A Z-score will standardize the data, only for normally distributed data
     • Standard normal: A curve that has a mean of 0 and a standard deviation of 0
     • Positive: that many SD above the mean
     • Negative: that many SD below the mean

6. Fitting quadratic models to data

   • Quadratic Regression
     • Least- squares parabola, can be influenced by outliers
   • Matrix Method
     • Only uses three points and is not influenced by outliers

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