2.3 - 2.4 Percentiles, Box Plots, z-Scores

Question 1

What is the p^th percentile of a distribution?

Answer 1

the value such that p% of the observations are less than or equal to the value

Question 2

Define quartile. Identify Q1, Q2, and Q3. Define the interquartile range (IQR). What is the Interquartile Criterion for Outliers?

Answer 2

*percentiles that divide the data into fourths
*Q2 = median
*Q1 = median of the data less than Q2
*Q3 = median of the data greater than Q2
*Q3 - Q1; the difference between the first and third quartiles
*potential outliers fall more than 1.5 x IQR below the first quartile or more than 1.5 x IQR above the third quartile

Question 3

What is the five number summary for box and whiskers plots? What is the equation for IQR? What is the equation for outliers?

Answer 3

*min, A1, Q2, Q3, max
*Q3 - Q1
* < 1.5 x IQR below Q1
> 1.5 x IQR above Q3

Question 4

Define z-Score. Equation provided on formula sheet.

Answer 4

the number of standard deviations that an observation falls from the mean

Question 5

Define the Emperical Rule.

Answer 5

for a bell shaped distribution:
*68% of the data falls within 1 δ of the u
*95% of the data falls within 2 δ of the u
*99.7% of the data falls within 3 δ of u

Question 6

What is the Standard Deviation Criterion for Outliers?

Answer 6

potential outliers fall more than 3 standard deviations above or below the mean (1.5 x IQR)

Question 7

Define a misleading graph.

Answer 7

any graph that distracts the reader from fuly understanding what he/she is viewing
*vertical axis doesn’t start at 0
*relative size of the icons are different
*y-axis is collapsed