Construct a cumulative frequency distribution and an ogive for the data set using six classes. Then describe the location of the greatest increase in frequency.
Retirement Ages
Data set: Retirement ages of 35 English professors 72 62 55 61 53 62 65 66 69 55 66 63 67 69 55 65 67 57 67 68 73 75 65 54 71 57 52 58 58 71 72 67 63 65 61

Verified step by step guidance

1. Organize the data set in ascending order. This will make it easier to group the data into classes and calculate frequencies.
2. Determine the range of the data by subtracting the smallest value from the largest value. Then, divide the range by the number of classes (6 in this case) to calculate the class width. Round up to the nearest whole number if necessary.
3. Create six classes by starting with the smallest value and adding the class width to define the upper limit of each class. Ensure that the classes do not overlap and cover the entire range of the data.
4. Count the number of data points (frequencies) that fall into each class. Then, calculate the cumulative frequency for each class by adding the frequency of the current class to the cumulative frequency of the previous class.
5. Plot the ogive by graphing the cumulative frequencies on the y-axis and the upper class boundaries on the x-axis. To describe the location of the greatest increase in frequency, identify the steepest segment of the ogive, which corresponds to the class with the largest frequency increase.

Key Concepts

Cumulative Frequency Distribution

A cumulative frequency distribution is a statistical tool that summarizes the number of observations that fall below a particular value in a dataset. It is constructed by adding the frequency of each class interval to the sum of the frequencies of all preceding intervals. This allows for an understanding of the distribution of data points across different ranges, making it easier to identify trends and patterns.

Ogive

An ogive is a graphical representation of a cumulative frequency distribution. It is plotted with the cumulative frequency on the y-axis and the upper boundaries of the class intervals on the x-axis. The resulting curve helps visualize how many data points fall below a certain value, allowing for quick assessments of data distribution and comparisons between different datasets.

Class Intervals

Class intervals are the ranges into which data points are grouped for frequency distribution analysis. In this context, the data set is divided into six classes, which helps in organizing the data for cumulative frequency and ogive construction. Choosing appropriate class intervals is crucial, as it affects the clarity and interpretability of the distribution, highlighting areas of significant frequency changes.