Understanding Frequency Distributions & Data Analysis: Intervals, Limits, and Frequencies, Study notes of Probability and Statistics

Download Understanding Frequency Distributions & Data Analysis: Intervals, Limits, and Frequencies and more Study notes Probability and Statistics in PDF only on Docsity! 1 Chapter 2 Describing, Exploring, and Comparing Data Chapter 2 Describing, Exploring, and Comparing Data 2-1 Overview 2-2 Frequency Distributions 2-3 Visualizing Data 2-4 Measures of Center 2-5 Measures of Variation 2-6 Measures of Relative Standing 2-7 Exploratory Data Analysis (EDA) 2 -1 Overview 1. Center: A representative or average value that indicates where the middle of the data set is located 2. Variation: A measure of the amount that the values vary among themselves 3. Distribution: The nature or shape of the distribution of data (such as bell-shaped, uniform, or skewed) 4. Outliers: Sample values that lie very far away from the vast majority of other sample values 5. Time: Changing characteristics of the data over time Important Characteristics of Data 2 Descriptive Statistics summarize or describe the important characteristics of a known set of population data Inferential Statistics use sample data to make inferences (or generalizations) about a population 2 -1 Overview Frequency Table lists data values (either individually or by groups of intervals), along with their corresponding frequencies (or counts). 2-2 Frequency Distributions Qwerty Keyboard Word Ratings 2 2 5 1 2 6 3 3 4 2 4 0 5 7 7 5 6 6 8 10 7 2 2 10 5 8 2 5 4 2 6 2 6 1 7 2 7 2 3 8 1 5 2 5 2 14 2 2 6 3 1 7 Frequency Table of Qwerty Word Ratings 0 - 2 20 3 - 5 14 6 - 8 15 9 - 11 2 12 - 14 1 Rating Frequency 5 midpoints of the classes Class Midpoints midpoints of the classes Class Midpoints Class Midpoints 0 - 1 2 20 3 - 4 5 14 6 - 7 8 15 9 - 10 11 2 12 - 13 14 1 Rating Frequency Class Width is the difference between two consecutive lower class limits or two consecutive class boundaries Class Width Class Width 3 0 - 2 20 3 3 - 5 14 3 6 - 8 15 3 9 - 11 2 3 12 - 14 1 Rating Frequency is the difference between two consecutive lower class limits or two consecutive class boundaries 6 3. Select for the first lower limit either the lowest score or a convenient value slightly less than the lowest score. 4. Add the class width to the starting point to get the second lower class limit, add the width to the second lower limit to get the third, and so on. 5. List the lower class limits in a vertical column and enter the upper class limits. 6. Represent each score by a tally mark in the appropriate class. Total tally marks to find the total frequency for each class. Constructing A Frequency Table 1. Decide on the number of classes . 2. Determine the class width by dividing the range by the number of classes and round (up usually). class width ≈ Highest value – lowest value number of classes 1. Be sure that the classes are mutually exclusive, that is, do not overlap so each data value belongs to only one class. 2. Include all classes, even if the frequency is zero. 3. Try to use the same width for all classes, although sometimes open-ended intervals are necessary. The sum of the class frequencies must equal the number of original data values. Guidelines For Frequency Tables Relative Frequency Table relative frequency = class frequency sum of all frequencies Relative Frequency Table 0 - 2 20 3 - 5 14 6 - 8 15 9 - 11 2 12 - 14 1 Rating Frequency 0 - 2 38.5% 3 - 5 26.9% 6 - 8 28.8% 9 - 11 3.8% 12 - 14 1.9% Rating Relative Frequency 20/52 = 38.5% 14/52 = 26.9% etc. Total frequency = 52 Total percentage ≈ 100% 7 Cumulative Frequency Table Cumulative Frequencies 0 - 2 20 3 - 5 14 6 - 8 15 9 - 11 2 12 - 14 1 Rating Frequency Less than 3 20 Less than 6 34 Less than 9 49 Less than 12 51 Less than 15 52 Rating Cumulative Frequency Frequency Tables 0 - 2 20 3 - 5 14 6 - 8 15 9 - 11 2 12 - 14 1 Rating Frequency 0 - 2 38.5% 3 - 5 26.9% 6 - 8 28.8% 9 - 11 3.8% 12 - 14 1.9% Rating Relative Frequency Less than 3 20 Less than 6 34 Less than 9 49 Less than 12 51 Less than 15 52 Rating Cumulative Frequency