Statistics Visual Representation of Data Part 1 Tables

Warm-up A survey of 200 adults in the U.S. found that 76% regularly wear seatbelts while driving. True or false: 76% is a parameter. Consumer Reports’ ratings (Best Buy, Recommended, Not Recommended). What is the level of measurement? Determine whether the quantitative variable is continuous or discrete. The time (in minutes) required for a student to complete a quiz.

Warm-up True or false: The ATM pin numbers represent quantitative data. What type of study is depicted: A reading teacher wants to examine if a new reading program has been effective. She looks at test scores of a group of students enrolled in the program and compares them to students who were not in the program.

Agenda Warm-up Objective- To understand and construct an appropriate table for present data Summary Homework

When data is collected from a survey or designed experiment, they must be organized into a manageable form. Data that is not organized is referred to as raw data. Ways to Organize Data Tables Graphs Numerical Summaries

Objective 1 Organize Qualitative Data in Tables 2-6

A frequency distribution lists each category of data and the number of occurrences for each category of data. 2-7

EXAMPLE Organizing Qualitative Data into a Frequency Distribution The data on the next slide represent the color of M&Ms in a bag of plain M&Ms. Construct a frequency distribution of the color of plain M&Ms. 2-8

Frequency table 2-9

The relative frequency is the proportion (or percent) of observations within a category and is found using the formula: A relative frequency distribution lists the relative frequency of each category of data. 2-10

EXAMPLE Organizing Qualitative Data into a Relative Frequency Distribution Use the frequency distribution obtained in the prior example to construct a relative frequency distribution of the color of plain M&Ms. 2-11

Relative Frequency

Organize discrete data in tables 2-13 Objective 2

EXAMPLE Constructing Frequency and Relative Frequency Distribution from Discrete Data The following data represent the number of available cars in a household based on a random sample of 50 households. Construct a frequency and relative frequency distribution Data based on results reported by the United States Bureau of the Census. 2-14

2-15

Organize continuous data in tables 2-16 Objective 3

Categories of data are created for continuous data using intervals of numbers called classes. 2-17

Frequency Distribution A table that shows classes or intervals of data with a count of the number of entries in each class. The frequency, f, of a class is the number of data entries in the class. ClassFrequency, f 1 – 55 6 – – – – – 304 Lower class limits Upper class limits Class width 6 – 1 = 5

Guidelines for Constructing a Frequency Distribution There should be between 5 and 20 classes. There should be between 5 and 20 classes. The class width should be an odd number. The class width should be an odd number. The classes must be mutually exclusive. The classes must be mutually exclusive.

Guidelines for Constructing a Frequency Distribution The classes must be continuous. The classes must be continuous. The classes must be exhaustive. The classes must be exhaustive. The class must be equal in width. The class must be equal in width.

Constructing a Frequency Distribution 1. Decide on the number of classes. Usually between 5 and 20; otherwise, it may be difficult to detect any patterns. 2. Find the class width. Determine the range of the data. Divide the range by the number of classes. Round up to the next convenient number.

Constructing a Frequency Distribution 3. Find the class limits. You can use the minimum data entry as the lower limit of the first class. Find the remaining lower limits (add the class width to the lower limit of the preceding class). Find the upper limit of the first class. Remember that classes cannot overlap. Find the remaining upper class limits.

Constructing a Frequency Distribution 4. Make a tally mark for each data entry in the row of the appropriate class. 5. Count the tally marks to find the total frequency f for each class.

Example: Constructing a Frequency Distribution The following sample data set lists the number of minutes 50 Internet subscribers spent on the Internet during their most recent session. Construct a frequency distribution that has seven classes

Construct Raw Score Frequency Distribution Value f Value f

Solution: Constructing a Frequency Distribution 1. Number of classes = 7 (given) 2. Find the class width Round up to

Solution: Constructing a Frequency Distribution Lower limit Upper limit 7 Class width = 12 3.Use 7 (minimum value) as first lower limit. Add the class width of 12 to get the lower limit of the next class = 19 Find the remaining lower limits

Solution: Constructing a Frequency Distribution The upper limit of the first class is 18 (one less than the lower limit of the second class). Add the class width of 12 to get the upper limit of the next class = 30 Find the remaining upper limits. Lower limit Upper limit Class width =

Solution: Constructing a Frequency Distribution 4. Make a tally mark for each data entry in the row of the appropriate class. 5. Count the tally marks to find the total frequency f for each class. ClassTallyFrequenc y, f 7 – 18IIII I6 19 – 30IIII – 42IIII IIII III13 43 – 54IIII III8 55 – 66IIII5 67 – 78IIII I6 79 – 90II2 Σf = 50

Determining the Midpoint Midpoint of a class ClassMidpointFrequency, f 7 – – – 4213 Class width = 12

Determining the Relative Frequency Relative Frequency of a class Portion or percentage of the data that falls in a particular class. ClassFrequency, f Relative Frequency 7 – – – 4213

Determining the Cumulative Frequency Cumulative frequency of a class The sum of the frequency for that class and all previous classes. ClassFrequency, fCumulative frequency 7 – – –

Expanded Frequency Distribution ClassFrequency, f Midpoint Relative frequency Cumulative frequency 7 – – – – – – – Σf = 50

Try One! The following are the scores of 25 students on a statistics exam. Create a grouped frequency distribution: 60, 62 65, 67, 70, 71, 72, 72, 75, 75, 78, 78, 80, 82, 82, 84, 84, 84, 85, 87, 89, 90, 92, 93, 95 60, 62 65, 67, 70, 71, 72, 72, 75, 75, 78, 78, 80, 82, 82, 84, 84, 84, 85, 87, 89, 90, 92, 93, 95

Summary Putting data into tables Qualitative Data Discrete Data Continuous Data

Homework Pg 43-45, # 1 – 12