STA 1063C Lecture Notes - Lecture 10: Standard Deviation, Descriptive Statistics, Summary Statistics

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6 Feb 2017
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Shapes of Distributions
o Symmetric: same on either side of the highest point in the middle (bell curve)
o Uniform: all observations occur the same amount of times
In symmetric data, mean=median
o Skewed right- most data is over to the left of the graph
Mean > median
o Skewed left- most data is over to the right of the graph
Mean < median
o Example: how will the following data sets be distributed?
A. Grades on an easy test- skewed left, mean < median
B. Grades on a difficult test- skewed right, mean > median
C. Number of days spent in the hospital last year- skewed right, mean >
median
D. Scores on SAT/ACT- symmetric, mean=median
Measures of variation
o Range: max-min
o The deviation for each value x is the difference between the value of x and the
mean of the data set
Example: 4, 6, 11
Mean: 7
4-7= -3; 6-7= -1; 11-7= 4
Deviation always adds to be 0; need a different measure of variation
o Squares of deviations
sum of (x-mu) squared/N --N= population size
Note: units are squared
Standard Deviation: square root of the variance
sum of (x-xbar) squared/n-1 n= sample size
Example: (-3)sq. + (-1)sq. + (4)sq./2
S sq. = 13
Square root of 13= 3.61 (standard deviation)
The more spread the data set, the larger the standard deviation
If all your observations are the same, there will be no variation or standard
deviation (0)
Standard deviation is always greater than or equal to zero (positive)
Distributions on Excel
o Open new workbook and enter data
Label column A “data”
o Data tab > data analysis > descriptive statistics > select all data for input range >
new worksheet ply > select summary statistics
o Enlarge column by double clicking between A and B
o Go back to data sheet, enter deviations Use mean from descriptive statistics
Label column B “deviations”
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