Ch. 3 Flashcards
A value used to describe the central tendency of a set of data
Measure of location
What are some common measures of location
Arithmetic Mean, weighted mean, geometric mean, Median, and Mode
How big the variation or spread in data is
Dispersion
The most widely used and widely reported measure of location. Used as both population parameter and sample statistic
Arithmetic Mean
The sum of all values in a population divided by the number of values in the population.
Populations Mean
A characteristic of a population
Parameter
The sum of all the sampled values divided by the total number of sampled values.
Sample Mean
A characteristic of a sample
Statistic
The midpoint or center value after they have been ordered from the minimum to the maximum values
Median
For the median, what is the minimal level of measurement
Ordinal
What are major properties of the median
- It is not affected by extremely large or small values
- It can be computed at ordinal-level data or higher
The value of observations that appears most frequently
Mode
What’s the advantage of the mode
Extremely high or low values don’t affect its value
What are disadvantages of the mode
- There may not be a mode in some data sets
- There may be multiple modes (bimodal or multi-modal)
A value that shows the spread of a data set. The range, variance, and standard deviation are examples
Measures of dispersion
A convenient way to compute the arithmetic mean when there are several observations of the same value
The weighted mean
A set of n positive numbers computed as the nth root of the product of n values. Useful for finding average rates of change
The geometric mean
What is the formula for geometric mean for rate of increase over time
nth root for number of years of ending value divided by beginning value, then subtracting one from the answer.
The maximum - minimum values in a data set
The range
What is a limitation of the range
It only accounts for two values
The arithmetic mean of the squared deviations from the mean
The Variance
How do you calculate the variance
square the difference of the value - mean, divide the sum of the differences by the number of values
The square root of the population variance
Standard deviation
What’s the difference in formulas from population variance to sample variance
Denominator in population variance is n, in the sample variance, it’s n-1
For any set of observations, the proportion of the values that lie within k standard deviations of the mean is at least 1-1/k squared, where k is any value greater than 1.
Chebyshev’s Theorem
What is the empirical rule for symmetrical bell shaped frequency distribution
About 68% with be with +-1 standard deviations
About 95 percent will be with +-2 standard deviations
and about 99.7% will be within plus or minus 3 standard deviations
