Technical Mathematics, Sixth Edition

21.2. Frequency Distributions

21.2.1. Raw Data

Data that have not been organized in any way are called raw data. Data that have been sorted into ascending or descending order are called an array. The range of the data is the difference between the largest and the smallest number in that array.

Example 9: Five students were chosen at random and their heights (in inches) were measured. The raw data obtained were 56.2 72.8 58.3 56.9 67.5 If we sort the numbers into ascending order, we get the array 56.2 56.9 58.3 67.5 72.8 The range of the data is range = 72.8 − 56.2 = 16.6 in.

21.2.2. Grouped Data

For discrete and categorical data, we have seen that x-y graphs and bar charts are effective. These graphs can also be used for continuous data, but first we must collect those data into groups. This process is especially helpful when working with a large number of data points. Such groups are usually called classes. We create classes by dividing the range into a convenient number of intervals. Each interval has an upper and a lower limit or class boundary. The class width is equal to the upper class boundary minus the lower class limit. The intervals are chosen so that a given data point cannot fall directly on a class boundary. We call the center of each interval the class midpoint.

21.2.3. Frequency Distribution

Once the classes have been defined, we may tally the number of measurements falling within each class. Such a tally is called a frequency distribution. The number of entries ...