2 1 2 2 Describing and Summarizing Data

2. 1 -2. 2: Describing and Summarizing Data Objective: To describe and summarize data using charts and tables

2. 1 -Describing, Exploring, and Comparing Data

Methods for Drawing Conclusions �Descriptive Statistic: to summarize or describe the important characteristics of a set of data (the results of data) �Example: �Inferential Statistics: we use these methods when we use sample data to make inferences or generalizations about a populations. �Example:

Examples: A survey conducted among 1017 men and women by Opinion Research Corporation International found that 76% of women and 60% of men had a physical exam the previous year. �What is the descriptive statistic? �What is the inferential statistic?

When describing, exploring, and comparing quantitative data sets, the following characteristics of data are usually most important:

2. 2 -Summarizing Data with Frequency Tables

What is a Frequency Distribution? �Lists classes (or categories) of values, along with frequencies (or counts) of the number of values that fall into each class � Lower class limits: the smallest numbers that belong to different classes � Upper class limits: the largest numbers that belong to different classes � Class boundaries: the numbers used to separate classes, but without the gaps created by class limits � � � Find the size of the gap between the upper limit of one class and lower limit of the next class Add half of that amount to each upper class limit to find the upper class boundaries Subtract half of that amount from each lower class limit to find the lower class boundaries � Class midpoints: midpoints of the classes found by adding the lower and upper limits of each class and dividing by 2 � Class width: the difference between two consecutive lower class limits

Steps to Creating a Frequency Distribution 1) Figure out class width: � Class Width = Max # - Min # # of classes (btw 5 -20) � Make it the next largest integer! 2) Set up Classes: � Start the first class with Min # � Add the class width to the Min # to get the next lower limit. � Continue to do this until you have the number of classes that are required. � Go back and create you upper limits (1 less than the next lower limit) � Last upper limit � Either add your class width to the previous upper limit or what would the upper limit be if there was another class.

Steps to Creating a Frequency Distribution 3) Make Tallies: �What class does the data piece fall into put a tally at that class. 4) Count tallies and put the number in frequency column. 5) Find the midpoint of each class. �Add the upper and lower class limits together and divide by 2. 6) Find the relative frequency for each class. The frequency in that class Total number of frequency

Steps to Creating a Frequency Distribution 7) Find the Cumulative Frequency �The sum of the frequency for that class and all the classes above.

Example �Example: Create a frequency distribution on the data given about time (in minutes) spent reading the newspaper in a day. �Data: 7 39 13 9 25 8 22 2 5 8 Classes Tallies 2 29 15 Frequency 18 3 12 Midpoint 2 11 35 30 39 Relative Frequency 7 16 6 15 Cumulative Frequency

Assignment � 2. 2 Worksheet