Read page 41 Do the Academy Awards involve discrimination based on age? What do you think?

Summarizing and Graphing Data Identify five important characteristics of data. Construct a frequency distribution, identify the class width, class midpoints, and the class boundaries.

Organizing, summarizing, and graphing sets of data. Ultimate Objective: UNDERSTAND TO DATA Important Characteristics of Data: Center Indicates the middle of the data set Variation Measures the amount that the data values vary among themselves Distribution Nature of shape of the distribution (normal “bell”, uniform, skewed) Outliers Sample values that lie very far away from the vast majority of the other sample values Time Changing characteristics of data over time

Computer Viruses Destroy Or Terminate As proceed through class, we will be performing a few manual calculations but the focus will be on obtaining results by using some form of technology.

Frequency Distribution Method of organizing large data sets Helps statistician to understand the nature of the distribution of a data set. Lists data values (either individually or by groups of intervals), along with their corresponding frequencies (or counts).

Look at table 2-2 on page 43 Frequency Distribution: Ages of Best Actresses Lower Class Limits: smallest numbers that belong to the different classes. Upper Class Limits: largest numbers that belong to the different classes. Class Boundaries: Numbers used to separate classes, but without gaps created by the class limits Class Midpoints: Values in the middle of the classes. Each class midpoint can be found by adding the lower class limit to the upper class limit and dividing the sum by 2 Class Width: Difference between two consecutive lower class limits or consecutive lower class boundaries Age of Actress Frequency 21-30 28 31-40 30 41-50 12 51-60 2 61-70 71-80 Lower class limits: 21, 31, 41, 51, 61, 71 Upper class limits: 30, 40, 50, 61, 70, 80 Class boundaries: 20.5, 30.5, 40.5, 50.5, 60.5, 70.5, 80.5 Class midpoints: 25.5, 35.5, 45.5, 55.5, 65.5, 75.5 Class with: 10

Be careful to avoid the mistake of making the class width the difference between the lower class limit and the upper class limit. Find class boundaries and find difference between class boundaries.

Constructing a Frequency Distribution Constructed for Three Reasons Large data sets can be summarized Gain some insight into the nature of the data Have a basis for constructing important graphs

Basic Procedure of Construction 1. Decide on the number of classes you want (should be between 5 and 20). 2. Calculate the class width (round to a convenient number. [Maximum value – Minimum value] number of classes 3. Find your starting point (minimum value or a convenient # below it) 4. Using the lower limit of the first class and the class width, proceed to list the other lower class limits. (Add the class width to the starting point to get the second lower class limit.)

5. List the lower class limits in a vertical column and proceed to enter the upper class limits. 6. Mark a tally in the appropriate class for each data value. Use the tally marks to find the total frequency for each class. Construct a frequency distribution for the best actors from the list on page 41 as a class. Follow the six steps. Number of classes, class width, starting point, lower limits, upper limits, tallies

Relative Frequency Distribution Includes same class limits but shows percentages rather than actual frequencies. Relative frequency: class frequency____ sum of all frequencies Find the relative frequency distribution for the best actors.

Cumulative Frequency Distributions Cumulative frequency is the sum of the frequencies of that class and all values below that class. Shows number at or below Find the cumulative frequency distributions for the best actor awards

Interpreting Frequency Distributions Important objective: to identify the nature of the distribution Normal (Bell) Shape Distribution: Uniform Distribution: Skewed Distribution

Look at table 2-5 on page 47. What type of distribution is this? What kind of distribution is the best actor frequency distribution?

Identifying other information from frequency distributions. Look at the frequency distributions on page 47 Look at the heart beat frequency table. Do you notice anything about the values? Pulses counted for 15 seconds and multiplied by 4 Penny frequency distribution – what could the gaps mean? Pennies from two populations; before 1983 and those after 1983 Can you recognize about actresses and actors from the frequency table? Actresses tend to be younger than actors.

Assignment Page 48 #1-14 all, 20, 22, 24