Ch 2; Describing Distributions w/ Numbers

Question 1

Using Numerical Summary of Distribution (2)

Answer 1

Center & Variability

Question 2

Measures of Center (2)

Answer 2

Mean (x̃) & Median (M)

Question 3

Mean

Answer 3

Ordinary arithmetic average. (Add values & divide by # of values) (x̃ = (x1, x2, …, xn) / n)

Question 4

Median

Answer 4

Midpoint of distribution. (# where 1/2 observations smaller & 1/2 observations bigger)

Question 5

How to Find M

Answer 5

1) Arrange observations from smallest to largest
2) Odd # observations (M is center observation), Even # observations (M is midway b/w 2 center observations)
3) Locate median by counting (n+1/ 2) observations from start of list

Question 6

Comparing Mean & Median in a Symmetrical Distribution vs a Skewed Distribution

Answer 6

Symmetrical; Mean & Median the same or very close

Skewed; Mean farther out in tail than median

Question 7

How to Measure Variability

Answer 7

Quartiles

Question 8

How to Find Quartiles

Answer 8

1) Arrange observations in increasing order & locate median
2) First Quartile is the median of observations to left of overall median
3) Third Quartile is the median of observations to right of overall median
4) If odd # median, leave out overall median when determining quartiles. If even # median use all observations.

Question 9

The 5 Number Summary

Answer 9

Consists of smallest observation, first quartile, median, third quartile, largest observation.

Question 10

Box Plot

Answer 10

A graph of the 5 number summary. Central box spans quartiles, line in box marks the median, lines extending from box go out to largest/smallest observations

Question 11

Interquartile Range (IQR)

Answer 11

Distance b/w Q1 & Q3 or range that encloses middle 50%.

Question 12

The 1.5 x IQR Rule for Outliers

Answer 12

Call an observations an outlier if falls more than 1.5 x IQR above Q3 or below Q1

Question 13

Resistant Measure

Answer 13

Any aspect of distribution relatively unaffected by changes in the numerical value of a small proportion of the total # of observations, no matter how large changes.

Question 14

Which Measures are Resistant (2)

Answer 14

Median & Quartiles

Question 15

Which Measures are Not Resistant (2)

Answer 15

Mean & Standard Deviation

Question 16

Standard Deviation (s)

Answer 16

Square Root of Variance (s^2)

Question 17

Variance (s^2)

Answer 17

Average of the squares of the deviations of the observations from their mean.

Question 18

Best Measures to Describe A Skewed Distribution/ Distribution w/ Strong Outliers

Answer 18

5# summary generally better than the mean & standard deviation.

Question 19

Best Measures to Describe a Symmetric Distributions that are Free of Outliers

Answer 19

Mean & standard deviation.

Question 20

Mode

Answer 20

Most frequently occurring value