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Understanding Frequency Distributions & Data Analysis: Intervals, Limits, and Frequencies, Study notes of Probability and Statistics

An overview of frequency distributions, including definitions of lower and upper class limits, class boundaries, and class midpoints. It also covers constructing a frequency table, relative frequency tables, and cumulative frequency tables. An extract from a statistics textbook and is intended for university students.

Typology: Study notes

Pre 2010

Uploaded on 08/17/2009

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Chapter 2
Describing, Exploring,
and Comparing Data
Chapter 2
Describing, Exploring, and
Comparing Data
2-1 Overview
2-2 Frequency Distributions
2-3 Visualizing Data
2-4 Measures of Center
2-5 Measures of Variation
2-6 Measures of Relative Standing
2-7 Exploratory Data Analysis (EDA)
2 -1
Overview
1. Center: A representative or average value that
indicates where the middle of the data set is located
2. Variation: A measure of the amount that the values
vary among themselves
3. Distribution: The nature or shape of the distribution
of data (such as bell-shaped, uniform, or skewed)
4. Outliers: Sample values that lie very far away from
the vast majority of other sample values
5. Time: Changing characteristics of the data over
time
Important Characteristics of Data
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Chapter 2

Describing, Exploring,and Comparing Data

Chapter 2

Describing, Exploring, andComparing Data

2-1 Overview2-2 Frequency Distributions2-3 Visualizing Data2-4 Measures of Center2-5 Measures of Variation2-6 Measures of Relative Standing2-7 Exploratory Data Analysis (EDA)

Overview

Important Characteristics of Data1. Center: A representative or average value thatindicates where the middle of the data set is located2. Variation: A measure of the amount that the valuesvary among themselves3. Distribution: The nature or shape of the distributionof data (such as bell-shaped, uniform, or skewed)4. Outliers: Sample values that lie very far away fromthe vast majority of other sample values5. Time: Changing characteristics of the data overtime

2

2 -1^ ™^ Descriptive Statisticssummarize or describe the importantcharacteristics of a known set ofpopulation data ™^ Inferential Statisticsuse sample data to make inferences (orgeneralizations) about a population

Overview

™^ Frequency Tablelists data values (either individually or bygroups of intervals), along with theircorresponding frequencies (or counts).

2- Frequency Distributions

Qwerty Keyboard Word Ratings 2 2 5

Frequency Table of Qwerty Word Ratings

0 - 2^

3 - 5^

6 - 8^

9 - 11^

12 - 14^

Rating^

Frequency

4

Upper Class Limits

0 - 2^

3 - 5^

6 - 8^

9 - 11^

12 - 14^

Rating^

Frequency

are the largest numbers that can actually belong todifferent classes

Upper Class Limits Upper ClassLimits

0 - 2^

3 - 5^

6 - 8^

9 - 11^

12 - 14^

Rating^

Frequency

are the largest numbers that can actually belong todifferent classes

Class Boundaries

0 - 2^

3 - 5^

6 - 8^

9 - 11^

12 - 14^

Rating^

Frequency

number separating classes

Class Boundaries

ClassBoundaries

0 - 2^

3 - 5^

6 - 8^

9 - 11^

12 - 14^

Rating^

Frequency

  • 0.52.55.5 8.511.514.

number separating classes

5

Class Midpoints midpoints of the classes

Class Midpointsmidpoints of the classes

ClassMidpoints

0 - 1^2

3 - 4^5

6 - 7^8

9 - 10 11^

Rating^

Frequency

Class Width is the difference between two consecutive lowerclass limits or two consecutive class boundaries

Class Width

Class Width

3 0 - 2^

3 3 - 5^

3 6 - 8^

3 9 - 11^

3 12 - 14^

Rating^

Frequency

is the difference between two consecutive lowerclass limits or two consecutive class boundaries

7

Cumulative Frequency Table

CumulativeFrequencies

0 - 2^

3 - 5^

6 - 8^

9 - 11^

12 - 14^

Rating^ Frequency

Less than 3

Less than 6

Less than 9

Less than 12

Less than 15

Rating

CumulativeFrequency

Frequency Tables 0 - 2^20 3 - 5^14 6 - 8^15 9 - 11^

12 - 14^

Rating^ Frequency

RelativeRatingFrequency0 - 2 38.5%3 - 5 26.9%6 - 8 28.8%9 - 11 3.8%12 - 14 1.9%

Less than 3

Less than 6

Less than 9

Less than 12 Less than 15 Rating^

CumulativeFrequency