Question: Use the following data, which represent test grades for 20 students on a recent exam, to construct…

Use the following data, which represent test grades for 20 students on a recent exam, to construct a frequency distribution with classes: (50-59), (60-69), (70-79), (80-89), (90-99). Also, construct a histogram for the data, separating the bars at 50, 60, 70, 80, 90 and 100.

78, 82, 98, 91, 67, 72, 84, 88, 90, 74, 75, 82, 86, 94, 68, 64, 72, 58, 92, 94

Solution

To construct the frequency distribution from the given data, we will count the number of grades that fall into each specified class. Given data: 78, 82, 98, 91, 67, 72, 84, 88, 90, 74, 75, 82, 86, 94, 68, 64, 72, 58, 92, 94 Classes and frequency count: 1. Class (50-59): - Numbers: 58 - Frequency: 1 2. Class (60-69): - Numbers: 67, 68, 64 - Frequency: 3 3. Class (70-79): - Numbers: 78, 72, 74, 75, 72 - Frequency: 5 4. Class (80-89): - Numbers: 82, 84, 88, 82, 86 - Frequency: 5 5. Class (90-99): - Numbers: 98, 91, 90, 94, 92, 94 - Frequency: 6 To construct a histogram, plot each class range on the horizontal axis and the corresponding frequencies on the vertical axis. Separate the bars at 50, 60, 70, 80, 90, and 100. The height of each bar corresponds to the frequency of the class.