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What r the 3 different measures to describe the center of a set of data?


Median?
 Central location. gives you the middle where 50% of the numbers lie on each side.
 *When there is an even # of observations, the median is determined by averaging the 2 observations in the middle.

Mode?
the observation with the greatest frequency

Why is Mode not a good measure to use?
 In small samples not a good measure to use
 it may not be unique

How do you compute mean, median and mode on excel using one button?
Data Anaylsis > Descriptive Statistics (then input the range of numbers) > Summary statistics.

Which central measure is best?
Mean is used most often, but median could be better because it is not sensitive to extreme values.

When to compute Mean?
 Interval data
 u want to describe a single set of data

When to compute Median?
 Interval or Ordinal data (w/extreme observations)
 Describe a single set of data
Ordinal data  categorized with meaning

Range
Largest observation  Smallest observation
pg. 106

What are the measures of variability for interval data only?
 Range
 Variance
 Standard Deviation
 Coefficient of Variation

Is Variance a good way to explain a set of data? What could it tell us when compared to another set of data?
No, cuz it only gives us a rough idea of the variation in the data. Comparing to another set of data it could tell us if the 1st set of data has more variation than the 2nd set.

Variance interpretations are problematic cuz we squared the deviations to get the mean. How do you fix this problem?
you calc the standard deviation. Units associated with SD is the unit of the original data set.
pg. 110

How do U interpret Standard Deviation?
 Empirical Rule  Bell Shape
 Chebysheff's Theorem  all shapes

Empirical Rule
Ex: histogram is bell shaped. mean and SD are 10% and 8%. Interpret
 68% fall in between 1 SD, so 18% and 2%
 95% fall in between 2 SD, so 26% and 6%
 99.7% fall in between 3 SD

Chebysheff's Theorem
 provides lower bounds
 75% lie between 2 SD
 88.9% lie between 3 SD

Coefficient of Variation
Indicates whether the SD (variation) is large or small compared to the number of observations.
SD / by their mean

How do you word the Chef theorem?
 At least 75% of the numbers lie between
 At least 88.9% of the numbers lie between

