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Spell out your full name (first, middle and last) Be ready to share the following counts:Number of letters in your full name.

Number of vowels Number of consonants

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Section 2-1

Organizing Data

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After completing chapter 2, you should be able to

Organize data using frequency distributionRepresent data in frequency distributions graphically using histograms, frequency polygons, and ogive

Represent data using Pareto charts, time series graphs, and pie graphs.

Draw and interpret a stem and leaf plot.

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Objective 1: Organize data using frequency distributions.

Each raw data value is placed into a quantitative or qualitative category called a class.

The frequency of a class is the number of data values in a specific class.

When data are collected in the original form, they are called raw data.

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0011 0010 1010 1101 0001 0100 1011Frequency Distributions

A frequency distribution is the organization of raw data in table form, using classes and frequencies.

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A categorical frequency distribution is used for data that can be places in specific categories, such as nominal or ordinal level data.

Categorical Frequency Distribution

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0011 0010 1010 1101 0001 0100 1011Example 2-1

• Twenty-five army inductees were given blood test to determine their blood type. The data set is:

Construct a frequency Distribution

A B B AB OO O B AB BB B O A OA O O O AB

AB A O B A

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0011 0010 1010 1101 0001 0100 1011Make a Table

Blood Type

Tally Frequencyf

Relative frequency; %

A

B

AB

O

n= total number of values %100% nf

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0011 0010 1010 1101 0001 0100 1011Grouped Frequency Distributions

• When a range of data is large, the data must be grouped into classes that are more than one unit in width, in what is called a Grouped Frequency Distribution.

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Number of hours boat batteries last:

Class limits Class boundaries

Frequency Cumulative frequency

24-30 3

31-37 1

38-44 5

45-51 9

52-58 6

59-65 1

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0011 0010 1010 1101 0001 0100 1011Vocabulary

•Lower Class Limit

•Upper Class LimitLower and upper class limits should have the same number of decimal points as the raw data.

Range:

R= maximum value – minimum value

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0011 0010 1010 1101 0001 0100 1011Class boundaries

Class boundaries are used to separate the classes so that there is no gap in frequency distribution.

Class boundaries should have one more decimal place value than the raw data. Class boundaries always end in a 5

How to find the boundaries:

Lower limit – 0.5= lower boundary

Upper limit + 0.5=upper boundary

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0011 0010 1010 1101 0001 0100 1011More terms to know

• Class Width is difference between lower and upper class limits.

• Class Midpoint Xm

2upperlowerX m

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0011 0010 1010 1101 0001 0100 1011Make a Table

Class Tally Frequencyf

Relative frequency; %

n= total number of values %100% nf

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0011 0010 1010 1101 0001 0100 1011Example 2-2

• These data represent the record high temperatures (F) for each of the 50 states. Construct a grouped frequency distribution for the data using 7 classes.

112 100 127 120 134 118 105 110 109 112

110 118 117 116 118 122 114 114 105 109

107 112 114 115 118 117 118 112 106 110

116 108 110 121 113 120 119 111 104 111

120 113 120 117 105 110 118 112 114 114

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0011 0010 1010 1101 0001 0100 1011Solution to 2-2

Step 1: determine the classes by following the steps outlined below:

Find the Range.

The range, R=maximum value- minimum value

Select the number of classes desired; usually between 5 and 20

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Find the class width:

Round UP to the nearest whole number

Start with lower class limit, usually the lowest value, keep adding the width until you have the desired number of classes.

𝒘𝒊𝒅𝒕𝒉=𝑹

𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒄𝒍𝒂𝒔𝒔𝒆𝒔

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The values you have obtained are the lower class limits. Determine the upper class limits for each class but subtracting one from the lower class limit of the next class.

Determine the each class boundary.

Step 2: Now start the tallying process.

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To construct a frequency distribution follow these rules. (pg 38)1) There should be 5-20 classes.2) The class width should be an odd

number.3) Mutually exclusive4) Continuous5) Exhaustive6) Equal in width

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0011 0010 1010 1101 0001 0100 1011Ungrouped Frequency Distribution

• When the range of the data values is relatively small, a frequency distribution can be constructed using single data values for each classes. This type of distribution is called an ungrouped frequency distribution.

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0011 0010 1010 1101 0001 0100 1011Example 2-3

• A data shown here represent the number of miles per gallon that 30 selected four-wheel-drive sports utility vehicles obtained in city driving. Construct a frequency distribution and analyze it.

12 17 12 14 16 1816 18 12 16 17 1515 16 12 15 16 1612 14 15 12 15 1519 13 16 18 16 14

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0011 0010 1010 1101 0001 0100 1011Page 44

Procedure Table

And then on the next page:

5 reasons for constructing frequency distribution

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0011 0010 1010 1101 0001 0100 1011Homework

• Applying Concepts page 45 make sure to answer all questions.

• Exercises 2.1 page 46 #5, 7 and 13.• Use graph paper and ruler.