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Date:
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Section 5.7, Describing Spread: The Standard Deviation
Guided Notes
Directions: Fill in the blanks and answer any questions as you read along with Section 5.7, Describing
Spread: The Standard Deviation in your text book (FAPP p. 195-198).
THE NORMAL CURVE
68-95-99.7 Rule
+/- 1 Standard Deviation: 68%
+/- 2 Standard Deviation: 95%
+/- 3 Standard Deviation: 99.7%
This curve is used for sampling in mathematical statistics
Notes: Stem Plots
Stem plot
o A display of the distribution of a variable that attaches the final digits of the observation as
leaves on stems made up of all but the final digit, usually for small sets of data only. Stem plots
look like histograms on the
Notes: Standard Ballots
A standard ballot is a ballot that lists choices (or candidates) and the voter selects one.
There are two types of standard ballots:
1. Majority Rules
a. Majority rules ballots have exactly 2 candidates.
b. The voter must select on
Ordinal Ballots- ask the voters to rank their preferences by assigning a number to each
candidate.
Preference Schedule- The finished list ranking each voters preferences
There are two ways ordinal ballots can be done:
-with indifference (can have ties bet
Notes: Measures of Centricity
Two Ways to Describe the Center: Mean and Median
o Mean average value
Ordinary arithmetic average of a set of observations, average value.
To find mean of a set of observations, add their values, (x1, x2 , , xn) and divide
Notes: Constructing a Histogram
Histogram: The graph of the distribution of outcomes (often divided into classes) for a single variable.
Steps in Making a Histogram
o Choose the classes by dividing the range of data into classes of equal width.
o Count
Hamilton Method of Apportionment
I. To apportion with Hamiltons method, we require the following information:
1. Number of individuals in each category (state, county, grade, etc) as well as the whole
group (country, state, school).
2. How many total repr
Name:
Discrete Math Final Exam Review Questions
Number Theory
1. Add the following base 2 numbers in base 2: 101101 + 111 =
. =3 %
2mm 1
1% l
g 1 {:21 33%
1
2. Subtract the following base 2 numbers in bggse 2: 10011 101 = a E 2
a 9%
335W
1
Wm
M
Cardinal Ballots
Cardinal Ballot- asks voters to rank their choices on a predetermined scale. This might tell you
that a person likes one option only a little more than another but WAY more than a third option.
For instance- Rank each pizza choice on a sc
Notes: 5 Number Summary
Include Spread and Center to Better Describe a Distribution
o Range States the smallest and largest observations.
o Quartiles The center and the middle of the top and bottom halves
Calculating the Quartiles
o Arrange the observatio