Spell out your full name (first, middle and last)

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1 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

2 Section 2-1 Organizing Data

3 After completing chapter 2, you should be able to Organize data using frequency distribution Represent 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.

4 Objective 1: Organize data using frequency distributions. When data are collected in the original form, they are called raw data. 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.

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

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

7 Example 2-1 Twenty-five army inductees were given blood test to determine their blood type. The data set is: A B B AB O O O B AB B B B O A O A O O O AB AB A O B A Construct a frequency Distribution

8 n= total number of values Make a Table f % 100% n Blood Type Tally A B AB O Frequency f Relative frequency; %

9 Grouped 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.

10 Number of hours boat batteries last: Class limits Class boundaries Frequency Cumulative frequency

11 Vocabulary Lower Class Limit Upper Class Limit Lower and upper class limits should have the same number of decimal points as the raw data. Range: R= maximum value minimum value

12 Class boundaries Class boundaries are used to separate the classes so that there is no gap in frequency distribution. How to find the boundaries: Lower limit 0.5= lower boundary Upper limit + 0.5=upper boundary Class boundaries should have one more decimal place value than the raw data. Class boundaries always end in a 5

13 More terms to know Class Width is difference between lower and upper class limits. Class Midpoint X lower upper m X m 2

14 n= total number of values Make a Table Class Tally Frequency f f % 100% n Relative frequency; %

15 Example 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

16 Solution 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

17 Find the class width: width = R number of classes 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.

18 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.

19 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 exclusive 4) Continuous 5) Exhaustive 6) Equal in width

20 Ungrouped 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.

21 Example 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

22 Page 44 Procedure Table And then on the next page: 5 reasons for constructing frequency distribution

23 Homework Applying Concepts page 45 make sure to answer all questions. Exercises 2.1 page 46 #5, 7 and 13. Use graph paper and ruler.