MMW FINALS

a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data

statistics

involves methods of organizing, summarizing and presenting data

descriptive statistics

involves methods of using information from a sample to draw conclusions about the population

inferential statistics

refers to all the members of the subject of interest

population

result of a population

parameter

refers to selected the members of the subject of interest

sample

result of a sample

statistics

_______ are measured

variables

_______ are fixed

constants

in a ______ data presentation, results are presented in declarative form.

textual

in a ______ data presentation, results are tables, composed of rows and columns.

tabular

in a ______ data presentation, results are presented in diagrams.

graphical

________ are used for comparison of means, counts or percentages between two or more groups

bar graphs

______ are used to observe trends and gaps between categories per unit of time

line graphs

______ are used to describe parts of a whole

pie graphs

describes the relationship of two quantitative variables

scatterplots

presents statistical information with respect to geographical location

statistical maps

ratio and interval are

quantitative

nominal and ordinal are

qualitative

numerical variable with absolute zero

ratio

numerical variable with relative zero

interval

categorical variable with order

ordinal

categorical variable with no order

nominal

mean is also known as the

mathematical average

median and mode are also known as the

positional average

measures of central tendencies are known as

average

the sum of observations divided by the number of observations

arithmetic mean

the middle value of the ordered observations

median

the most frequent observation

mode

mean, median, and mode can be used for

interval/ratio

only median and mode can be used for

ordinal

only mode can be used for

nominal

Also known as “quantiles”

Measures of Other Positions

the difference between the lowest & highest observations

range

the difference between the Q1 and Q3

interquartile range

1st quartile

25%

3rd quartile

75%

in a boxplot, outliers are displayed as

dots

the average distance of each observation to the mean

mean absolute deviation

The total area under the curve

1

The interval μ±σ contains approximately ____ of the measurements.

68%

The interval μ±2σ contains approximately ____ of the measurements.

95%

The interval μ±3σ contains approximately ____ of the measurements.

99.7%

the number of standard deviations that X is away from the mean

z-score

To determine the equation of the best-fit line (least squares error)

simple linear regression

Equation of the best fit line

Y = a + bX

To determine the direction and magnitude of the linear relationship between two quantitative variables, X and Y.

correlation

.90 to 1.00 (positive or negative)

very high positive/negative correlation

.70 to .90 (positive or negative)

high positive/negative correlation

.50 to .70 (positive or negative)

moderate positive/negative correlation

.30 to .50 (positive or negative)

low positive/negative correlation

.00 to .30 (positive or negative)

negligible correlation

The act of dividing items between different groups according to some plan, especially to make proportionate distribution in a fair manner

apportionment

ratio of the total population to the total number of seats to be allocated

standard divisor (d)

ratio of a state’s population to the standard divisor

standard quota (q)

standard quota rounded down to the nearest whole number

lower quota

standard quota rounded up to the nearest whole number

upper quota

If the standard quota is an exact integer, then the lower quota equals the

standard quota

First apportionment method to be approved in the United States of America Congress, but was vetoed by President George Washington in 1792

Hamilton’s Method

Hamilton’s method was used to

apportion the US House of Representatives every ten years between 1852 and 1900

First used in US Congress in 1792 until 1840

Jefferson’s method

Increasing the number of seats may cause a party to lose a seat

Alabama Paradox

proposed using a modified divisor greater than the standard divisor, and he rounded his modified quotas quota up to the upper quota

john quincy adams

adams’ method tends to favor smaller states

true

Used by the US Congress in 1842 to 1852, 1911 and 1931

webster’s method

Currently being used to apportion the seats in the US House of Representatives since 1941

huntington-hill method

Never been used in the US Congress

lowndes’ method

Uses the harmonic mean (instead of the geometric mean that’s being used in the Hill- Huntington’s method)

dean’s method

Rounds off the standard quota using 0.4 as the cut-off (instead of the usual 0.5)

condorcet’s method

the action or process of indicating choice, opinion, or will on a question, such as the choosing of a candidate, by or as if by some recognized means, such as a ballot

voting

the goal of voting

consensus