Chapter 3 - Analyzing Flashcards
What is the definition for Central Tendency?
Extent to which the values of numbers group around a central value.
Central or typical value for a probability distribution
What are the three main categories for central tendencies?
Arithmetic Mean - Average
Median - Middle value with 50% above and 50% below
Mode - most occurring
What is the formula for the mean, and what values drastically affect the overall mean?
Mean - average of all the values
Sum of all values / number of values
It is affected by extreme values or outliers
What is the formula to calculate the median of an odd number of values?
How do you calculate the median of an even number of values?
Median for Odd = (n + 1) / 2
Median for Even = (n + 1) / 2 then average the two numbers on both sides of the value
When given a population with extreme outliers, is it better to calculate central tendency with the mean or the median?
Median
What is the definition of a variation of central tendency?
If the average class grade is 80 percent with a large variance, what does that mean?
The amount of scattering away from a central value
This means, although the average grade is 80 percent, the highest and lowest grades are far from 80
What are the four different ways you can measure variation?
Range
Sample Variance
Standard Deviation
Coefficient of Variation
What is the formula to calculate the Range?
X largest – X smallest
What is the formula to calculate the Variance?
S^2 = [(n ∑ (i=1)) (Xi-¯X )^2 ]
/ (n-1)
What is the formula to calculate the Standard Deviation?
S = √[(n ∑ (i=1)) (Xi-¯X )^2]
/ (n-1)
What is the formula for the Coefficient of Variation?
CV = (S / ¯X) ⋅ 100%
What do we use to calculate extreme outliers, and what is the formula?
Z-Score locates extreme outliers
Z = (X-¯X ) / S
x = current data value x-bar = sample mean S = sample standard deviation
What are the three different skews of a distribution, and what do each have to do with mean and median?
Left-Skew = mean < median - length is longer on the left
Symmetric = mean = median
Right-Skew = mean > median - length is longer on the right