Statistics FInal Review: True/False/Uncertain Question 2
Q1, Q2, Q3, Q4: Finding Q2
2(N+1)/4
Q1, Q2, Q3, Q4: Finding Q3
3(N+1)/4
Mean Absolute Deviation
MAD = ∑Ixi-μI N
∑
summation sign
Comparison of Measures: Relative Sizes
symmetry and skewness
Standard Deviation: Definition
the (positive) square root of the variance
Median
the data value that has as many observations above it as below it
Range
the difference between the highest and lowest values
Interquartile Range
the difference between the third and first quartiles (Q3-Q1)
The Greater the Dispersion
the less useful are measures of central tendency
With Skewness, the Most Representative Measure of Central Tendency is:
the median
N
the number of data values in the population
n
the number of data values in the sample
Arithmetic Mean
the sum of the data values divided by the number of observations
Mode
the value that occurs with the greatest frequency (single, most typical value)
Comparison of Measures
usefulness and relative sizes
wi
weight given to the ith data value
Interpolate
when the median is halfway between the two values in the middle
Population Mean
μ = ∑ xi N
Standard Deviation: Equation
population: σ = √σ² sample: s = √s²
Variance: Equation
population: σ² = ∑(xi-μ)² N _ sample: s² = ∑(xi-x)² n-1
Q1, Q2, Q3, Q4: Finding Q1
(N+1)/4
Comparison of Measures: Usefulness
-mean uses all the information, but is affected by extremes -mean and median are unique, but not the mode -mode is usually less useful, but the mean and median may not actually exist in the data set
Variance: Definition
-the average of the squared deviations from the mean -includes all data values
Measures of Dispersion
1) range 2) midrange 3) quantiles 4) interquartile range 5) quartile deviation 6) variance 7) standard deviation
Sample Mean
_ x = ∑ xi n
Residual
_ xi-x
Weighted Mean
_ μw or xw = ∑ wixi ∑ wi
xi
a particular data value (for i)
Midrange
average of the lowest and highest values
Quantiles
divides the data into parts (ex percentiles, deciles, quartiles)
Skewness
either positive (tails off to the right) or negative (tails of to the left)
Quartile Deviation
half the interquartile range (Q3-Q1)/2
Symmetrical Distributions
have the left and right sides that are mirror images
Bimodal
if there are two modes
Positively Skewed if:
mean > median > mode
Measures of Central Tendency
mean, median, mode
Negatively Skewed if:
mode > median > mean
Effect of Extreme Values on Median
no effect (good and bad)
