Describing Data Flashcards
Mean
average of a set of data
Median
the middle measurement in a set of ordered data
Mode
Most frequent measurement
Range
diff between smallest and largest value in data set (big minus small)
Why no range?
Small samples give lower estimates of the range than large samples, therefore sample range is a BIASED ESTIMATOR of the true range of a population.
Other measures have mathematical properties that help us understand samples sampling properties.
Variance
Specific equation
average squared deviation from the mean of a variable
= sigma^2
lower case sigma (letter o with a hat)^2
true value of variance in population
Standard Deviation
square root of the variance = sigma
Yi
value of this variable for the ith individual
LOOK AT VARIANCE EQ
SAMPLE VARIANCE EQUATION - what is it?
Best estimate of population variance for a set of data
sum of squares
sum of the squared deviations from the mean
sum of (Yi - Ybar)^2 value for every individual
greater standard deviation means:
greater variation
Coefficient of variation
standardizing variation by the mean
CV = 100% S/(Ybar)
accounts for differences in scale experienced in population
ex. 1cm ^ difference for mice than giraffes
Skew
measurement of asymmetry
Right skewed - long thing sticking out part on right side
Left skewed - long thing stickout out on LEFT side
adding a constant regarding mean
Mean[X + c] = Mean[X] + c
adding a constant regarding variance
constant has no impact on variance!
multiplying a constant regarding mean
Mean[xX]= cMean[X]
multiplying by a constant regarding variance
Var[c*X] = c^2 * Var[X]
larger sample =
closer to the truth
