The following distribution gives daily income of 50 workers in a factory. Convert the distribution to a less-than-type cumulative frequency distribution, then draw its ogive.
A less than type of cumulative frequency means that we want to take our class boundaries, in this case the daily income, and look at the number of workers who aren’t that amount or less. In a table, we take the class, the daily income, and then we’d want the cumulative frequency of each class. The lower end of our first class is 100.
In our chart, we want to know how many workers are in the less than 100. We have zero workers in that category. From there, we move to the upper bound of that class and ask how many workers are in the less than 120. We see that 12 workers are in the less than 120. Our next class would be the upper bound of 140. And the people that are in the less than 140 are all the people in the previous categories, 12 plus 14, a cumulative frequency of 26. The upper bound of our next category, less than 160, we need to add 12 plus 14 plus eight. The cumulative frequency, the number of people who are in the less than 160, is 34. Moving on, we want to know how many people are in the less than 180. That would be 12 plus 14 plus eight plus six. 40 people are in the less than 180.
The upper bound of our final category is 200. How many workers are in the less than 200? Which would include all of the workers in this table. 50 workers are in the less than 200. Now we need to turn this information into a graph.
But what belongs on each axis? The cumulative frequency goes along the 𝑦-axis, and the class boundaries go along the 𝑥-axis. But we want to label the 𝑥- and 𝑦-axis with our specific information. And our cumulative frequency is a measure of the number of workers, and our class boundaries are measures of daily income.
And we can turn our table into coordinates. Our first point is at 100, zero; then 120, 12; 140, 26; 160, 34; 180, 40; and 200, 50. The range of our 𝑥-axis, the range of daily income, is from 100 to 200. If we start the 𝑥-axis at 100, I’ll maybe count by twenties: 120, 140, 160, 180, and 200. This lines up nicely with our income boundaries.
For the 𝑦-axis, we start at zero and work our way up to 50. And we’ll label the graph as such: 10, 20, 30, 40, 50. Our first point, 100, zero, falls along the 𝑥-axis. Next, we have 120, 12 followed by 140, 26, followed by 160, 34; 180, 40; and then 200, 50. In an ogive, you need to connect each point with the line. This is what an ogive for the given information would look like.