🗊Презентация Types of Data – (continued). Week 2 (2)

BBA182 Applied Statistics Week 2 (2) Types of Data – (continued) Dr Susanne Hansen Saral Email: susanne.saral@okan.edu.tr https://piazza.com/class/ixrj5mmox1u2t8?cid=4# www.khanacademy.org

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Organizing categorical data Categorical data produce values that are names, words or codes, but not real numbers. Only calculations based on the frequency of occurrence of these names, words or codes are valid. We count the number of times a certain value occurs and add the frequency in the table.

The Frequency and relative frequency - Distribution Table Summarizing categorical data A frequency table organizes data by recording totals and category names. The variable we measure here is the number of times a country became world champion in football:

Contingency table another type of frequency table Contingency tables list the number of observations for every combination of values for two categorical variables

Contingency table A larger retailer of electronics conducted a survey to determine consumer preferences for various brands of digital cameras. The table summarizes responses by brand and gender: Each cell in a contingency table (any intersection of a row and column of the table) gives the count for a combination of values of two categorical variables

Three Rules of Data Analysis Rule 1, 2 and 3: Make a picture of the data Pictures…. Reveal things that cannot be seen in a frequency table Show important patterns in the data Provide an excellent way for presenting findings to other people

Bar Chart – Hospital patients

Pie Chart – Hospital patients

Bar-chart Number of visits to OKAN University website

Pie-chart Number of visits to OKAN University website

Graphing Multivariate Categorical Data Multivariate= more than one variable

Graphing Multivariate Categorical Data Side by side horizontal bar chart

Graphing Multivariate Categorical Data Stacked bar chart

Class exercise The following raw data show responses to the question “What is your primary source for news?” from a sample of college students: Internet Newspaper Internet TV Internet Newspaper TV Internet Internet TV Newspaper TV TV Newspaper TV Internet Internet Internet Internet Internet TV Internet Internet TV TV a. Prepare a frequency table for these data. How many students were sampled? b. Prepare a relative frequency table for these data. c. Based on the frequencies, construct a bar chart manually. d. What is the variable we are measuring?

Class exercise A cable company surveyed its customers and asked how likely they were to bundle other services, such as phone and Internet, with their cable TV subscription. The following raw data show the responses:

Week 2 (2) How to organize and illustrate numerical data Dr Susanne Hansen Saral Email: susanne.saral@okan.edu.tr or susannehansensaral@gmail.com

Classification of Variables

Tables and Graphs to Describe Numerical Variables

Enron Corporation - energy trading company Energy trading company from 1985 – 2001 (then went bankrupt): Company grew steadily over the 15 years Stock price in 1985 $ 5/share. By the end of 2000 it was $ 89.75 At the end of 2000 the company was worth $ 6 billion At the end of 2001 the stock had fallen to $ 0.25! The company had lost 99% of it’s value Were there any warning signs in the data?

Enron Corporation - energy trading company Energy trading company from 1985 – 2001: Were there any warning signs in the data?

Enron Corporation - energy trading company Energy trading company from 1985 – 2001: Were there any warning signs about the fall of the stock price in the data? Hard to tell from the raw data Let’s follow the first rule of data analysis and make a picture of the data

Enron Corporation – frequency distribution

Why Use Frequency Distributions and graphs for numerical data? A frequency distribution is a way to summarize numerical data It condenses the raw data into ranges/intervals and allows for a quick visual interpretation of the data – a PICTURE The picture of numerical/quantitative data is called a histogram

Frequency Distributions What is a Frequency Distribution for numerical data? A frequency distribution is a table containing ranges/intervals within which the data fall and the corresponding frequencies with which data fall within each class or category

Frequency Distributions for numerical data Intervals for numerical data are not as easy to identify as for categorical data. Determining the intervals of a frequency table for numerical data requires answers to the following questions: How many intervals should be used? How wide should each interval be?

Raw data (sample of 110 employees in a production plant) Completion Times of a particular task (in seconds) for 110 employees 271 236 294 252 254 263 266 222 262 278 288 262 237 247 282 224 263 267 254 271 278 263 262 288 247 252 264 263 247 225 281 279 238 252 242 248 263 255 294 268 255 272 271 291 263 242 288 252 226 263 269 227 273 281 267 263 244 249 252 256 263 252 261 245 252 294 288 245 251 269 256 264 252 232 275 284 252 263 274 252 252 256 254 269 234 285 275 263 263 246 294 252 231 265 269 235 275 288 294 263 247 252 269 261 266 269 236 276 248 299

How to determine the number of intervals/classes A quick guide Sample size Number of intervals Fewer than 50 5 - 7 50 to 100 7 - 8 101 to 500 8 - 10 501 to 1,000 10 - 11 1,001 to 5,000 11 - 14 More than 5,000 14 - 20 Use at least 5 intervals but no more than 15-20 otherwise we loose the overview of the data

How to determine the interval width Each class/interval grouping has to have the same width Determine the width of each interval by

Employee completion time 110 employees’ time have been recorded and the plant supervisor needs to report to his manager how long on average his employees finish the job. We have 110 values ranging from 222 seconds to 299 We need to determine the number of intervals:

Employee completion time Determine width of interval: Interval width = Interval width = = 9.6 - rounded up to 10 Interval width = 10

Employee completion time Completion time (in seconds) Frequency Relative frequency % 220 – 229 5 4.5 230 – 239 8 7.3 240 – 249 13 11.8 250 – 259 22 20.0 260 – 269 32 29.1 270 – 279 13 11.8 280 – 289 10 9.1 290 – 300 7 6.4 Total 110 100 %

Histogram of employee completion times Absolute frequency

Histogram of employee completion times Relative frequency same graph as absolute frequency

Employee completion time Cumulative frequency

Histogram – Absolute frequency Enron: Change in stock price

Histogram – Relative frequency Enron: Change in stock price