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Terms in this set (10)
Arithmetic Mean
Computed by adding all values of the variable in the data set and dividing by the # of observations. Known as the Mean.
Value such that a histogram of the data is perfectly balanced, with equal weight on each side of the mean
Population Arithmetic Mean (pronounced mew)
Computed using all the individuals in a population. Known as a Parameter.
Sample Arithmetic Mean (pronounced x-bar)
Computed using sample data. Known as a statistic.
Greek and Roman Symbols
N= population size
n= sample size
Greek
Sigma ="add the terms"
i=shows that various values are distinct and does not serve as a math operation
M=Median
Mew symbol = Population Mean
x-bar symbol= Sample Mean
Median
Value that lies in the middle of the data when arranged in ascending order
Mode
The most frequent observation of the variable in a data set.
If there is only 1 instance of each variable, there is no Mode.
A data set can have more than one mode (Bimodal or Multimodal) A set that is multimodal is usually not reported.
Measures of Central Tendency
1) Mean (uses all the data;
Best used for Quantitative data and frequency distribution that is roughly symmetrical)
2)Median (relies only on the
position of the data;
Best used for Quantitative data when frequency distribution is skewed right or left )
3) Mode (used for Qualitative data;
used for quantitative data when "most frequent" observation is desired measure)
When is a statistic Resistant?
If extreme values (very large or small) relative to the data do not affect its value substantially.
The Median is resistant - the Mean
is not
(extreme values DO make a difference in the Mean)
Relation between Mean, Median, and Distribution Shape
Skewed right - Mean substantially larger than Median.
Skewed left - Mean substantially smaller than Median.
Symmetric - Mean roughly equal to Median (we would use the Mean in this case)
NOTE: Guidelines that work well for continuous data, but when using discrete data, they may not apply in all cases.
Measure of Central Tendency for data that are Nominal
Only the Mode can be computed, not Mean or Median.
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