2 Organization and Description of Data

Two Main Types of Data 1. Qualitative or categorical data 2. Numerical, quantitative, or measurement data. There are two types of numerical data: Discrete and Continuous.

Categorical Data When the characteristic under study is only classified in categories the resulting data are called categorical data. Example: The blood types of 40 persons who have volunteered to donate blood O O A B A O A A A O B O B O O A O O A A A A AB A B A A O O A O O A A A O A O O AB

Discrete Data A data set is discrete when it can be counted. Example: Number of items returned in 30 days

Continuous Data Data that can take any value. Example: Hours of Sleep for Fifty-nine Students

Discrete data is counted, Continuous data is measured

Question Consider the characteristics (a) Height of a skyscraper. (b) Favorite primary color. (c) Number of visits to a dentist last year. In each case, determine if the resulting data are categorical, discrete, or continuous.

Answer (a) Height of a skyscraper. (Continuous) (b) Favorite primary color. (Categorical) (c) Number of visits to a dentist last year. (Discrete)

Describing Categorical Data Frequency table Pie Chart Pareto Diagram

Describing Categorical Data A campus press polled a sample of 280 undergraduate students in order to study student attitude toward a proposed change in the dormitory regulations. Each student was to respond as support, oppose, or neutral in regard to the issue. The numbers were 152 support, 77 neutral, and 51 opposed.

Pareto Diagram

Graduate were asked to choose one of their personal habits that needed improvement. They were asked to first gather data on the frequency of the occurrence and the circumstances. Follows are data on fingernail biting over a two-week period.

Describing Discrete Data Frequency Table (Distribution) Histogram

Discrete Data

Describing Continuous Data Dot diagram (when the number of observations is less than 20 or 25) Frequency distribution and Histogram (larger number of observations) Stem-and-Leaf Display (when observations are two digit numbers)

Dot Diagram When the data consist of a small set of numbers. Example: The number of days the first six heart transplant patients at Stanford survived after their operations were: 15, 3, 46, 623, 126, observations

Dot Diagram

Frequency distribution When the data consist of a large number of measurements. Example: Hours of Sleep for Fifty-nine Students

Constructing a Frequency Distribution for a Continuous Variable 1. Find the minimum and the maximum values in the data set. 2. Choose intervals or cells of equal length that cover the range between the minimum and the maximum without overlapping. These are called class intervals, and their endpoints class boundaries. 3. Count the number of observations in the data that belong to each class interval. The count in each class is the class frequency or cell frequency. 4. Calculate the relative frequency of each class by dividing the class frequency by the total number of observations in the data: Relative frequency =Class frequency/Total number of observations

Histogram

Stem-and-leaf Usually when the observations are two-digit numbers. List the digits 0 through 9 in a column and draw a vertical line. These correspond to the leading digit. For each observation, record its second digit to the right of this vertical line in the row where the first digit appears. Finally, arrange the second digits in each row so they are in increasing order.

Stem-and-leaf Data: