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Study Guide

School

Ryerson UniversityDepartment

Quantitative MethodsCourse Code

QMS 102Professor

Nursel RuzgarStudy Guide

FinalThis

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QMS 102

FINAL EXAM

STUDY GUIDE

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Introduction to Statistics

Statistics is a way to connect raw data into usable information

(e.g. results from surveys)

You can use statistics to create information that can be used for decision making as well as

even in marketing.

Marketing - Target markets, advertisements etc.

Other forms of decision making - Risks in business ventures

There are 2 Different Branches of Statistics Used in Business:

Descriptive Statistics: Collecting raw data (numbers) and analyzing the information (stocks,

cash flow)

Inferential Statistics: Using data collected from a smaller group to infer a larger population -

drawing conclusions from a smaller group (focus groups)

e.g. estimation & hypothesis testing (will be discussed in term 2)

Types of Variables in Statistics:

Categorical (qualitative): variables that have values that only be placed into categories

Numerical (quantitative): variables that have values that represent quantities

There are 2 sub groups:

Discrete - arise from a counting process (countable)

Continuous - arise from a measuring process (not; measured characteristics)

Types of Data:

Nominal - facts on categorical information

Ordinal - contains a ranking order (looks like nominal)

Interval - also called quantitative/numerical but also contains a unit of measurement

Ratio - can be discrete/continuous also contains characteristics of interval data

There are different ways to show data:

Bar Graphs

Pie Chart

Tables (Summary & Contingency)

Pareto Chart (Stupid)

Stem & Leaf Display

etc.

*Stem & Leaf - Scale to the left/right or symmetrical analysis

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Stem and Leaf Displays & Visualizing Data

A Steam and Leaf Display Conveys Information About the Following Aspects of Data:

● identification of a typical or representative value

● extent of spread about the typical value

● presence of any gaps in the data

● extent of symmetry in the distribution of values

● number & location of peaks

● presence of any outlying values

Stem Rules:

● Stems range from 6-13 steams ONLY

● Stem values should be consecutive numbers/repeated numbers. Numbers may be

repeated 2 or 5 times

● Stem units must be indicated if the steam is not to be taken at face value (10, 100, 1000)

○ Face Value would be decimal

● One leaf must be associated with the first & last stem; in between it doesn’t matter

Leaf Rules:

● Leaf of each data value is the next single digit after the stem

○ On 2 time repeats, the leaves valued 0-4 is on the first stem, 5-9 on the second

stem

○ On 5 time repeats, leaves valued are broken apart with 2 digit values (0,1 first

stem, 2,3 second stem)

■ Orders are reversed for all situations when the stem has a negative value

● There is no rounding off for the values

○ Record value 876 with a defined stem of 8 must only be recorded as 7 (forget the

6)

● Leaf values are written in ascending order when positive, descending order when

negative

● Leaf values are evenly spaced

● No commas/dashes between the numbers allowed

Interpretation of Results

A) Using the stem & leaf plot to detect the shape of the data distribution

● Symmetry of a data distribution can be classified in 3 ways

○ Skewed to the left (bulk of data is on right [bottom])

○ Symmetrical (bulk of data is located in middle)

○ Skewed to the right (built of data is on the left [top])

B) Using the stem & leaf plot to extract information

● How many employees were sampled? (how many leaves there are)

● % of employees claimed at least/under ___ per ____? (any leaves over the particular

amount)

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