how do you construct a relative frequency table based on an ogive?
To construct a relative frequency table based on an ogive, you need to follow these steps:
1. Gather the data: Start with a set of data points for a given variable, such as the scores on a test.
2. Sort the data: Arrange the data in ascending order from smallest to largest.
3. Create a frequency table: Create a frequency table by dividing the data into intervals or bins. Determine the width of each interval, ensuring that it covers all the data points. For example, if the data range from 0 to 100, you might choose an interval width of 10 (e.g., 0-10, 10-20, etc.). Count the number of data points falling within each interval and record this count in the frequency column.
4. Calculate cumulative frequencies: Add up the counts in the frequency column from the smallest interval up to each interval, recording the cumulative frequency in a separate column.
5. Calculate relative frequencies: Divide the frequency count of each interval by the total number of data points. This will give you the relative frequency for each interval, which represents the proportion of data points falling within that interval.
6. Construct the ogive: In a new column, plot the cumulative frequencies on a graph by placing each value at the upper boundary of its corresponding interval. Connect the points with a line, starting from the leftmost point and ending at the rightmost point. This graph is called an ogive.
7. Construct the relative frequency table: Create a new table with columns for the intervals, frequency, cumulative frequency, and relative frequency. Fill in the intervals and corresponding frequency and cumulative frequency values from the frequency table. Add a new column for relative frequency and calculate the relative frequency for each interval by dividing the frequency of that interval by the total number of data points.
Now, you have a relative frequency table based on the ogive, which helps visualize the distribution and proportions of the data.