Cumulative frequency tables can help you analyze and understand large amounts of information.
In this lesson, you practice creating and interpreting cumulative frequency tables.
Cumulative Frequency Tables
Coach Bernard is starting his summer training for his football players. He wants to measure his players’ progress as the training continues.
He decides to record each player’s 40-yard dash at the beginning of the training and then time the players again at the end of the training. Here is a list of the times of the players:
Coach Bernard also wants to use this information to look at the overall performance of his team. He can use frequency and cumulative frequency tables to visualize and analyze this data.
Creating Cumulative Frequency Tables
It’s a bit overwhelming to look at this data as it is. We can organize all of this information into a frequency table. A frequency table is a chart that shows the popularity or mode of a certain type of data. When we look at frequency, we are looking at the number of times an event occurs within a given scenario.
In this case, we are looking at the frequency that a certain running time occurs.
In the frequency table above, Coach Bernard has listed the running times, in seconds, in the first column and the frequency that the times occur. You can see that each running time only occurs once, which means that each player has a different running time. This information is still pretty overwhelming to look at, and while you can see the range of running times, 4.
45 seconds to 7.24 seconds, it’s hard to gather anything else from this table. To make this data more informative, we can group the times into intervals.When constructing intervals, make sure that you are creating groups of information that are scaled and separated equally. In this case, we can start our frequency table at 4.01 seconds and end the table at 7.
50 like this:
Notice that each interval increases by approximately .49 seconds. The second column on the table above shows the number of players whose times fall within this range.This table gives us a better understanding of the speeds of the players. Now we can create a cumulative frequency table based on this information. A cumulative frequency table is a chart that shows the popularity or mode of a certain type of data and the likelihood that a given event will fall below the frequency distribution.
Let’s look at the frequency table we’ve already created. To make a cumulative frequency table, simply add the frequencies of each row and all of the rows above it.Still confused? Let’s do this one together. In the first interval we have 1 player that ran between 4.01 and 4.5 seconds. In the second row we have 3 players that ran between 4.
51 and 5.01 seconds. How many players ran faster than 5.01 seconds? That’s right! Four players ran faster than 5.01 seconds. We got this number by adding the first row and the second row together.
Let’s look at the 3rd row. How many players ran faster than 5.5 seconds? Eight. Eight players ran faster than 5.5 seconds.
We got that by adding the first three rows together. This is how you create and interpret a cumulative frequency table. This is what the rest of that table looks like:
First, let’s put this information into the same intervals as our first frequency chart, like this:
Now, add each row together to create a cumulative frequency table. This time, two players ran faster than 4.5 seconds, five players ran faster than 5.
01 seconds, ten players ran faster than 5.5 seconds, 12 players ran faster than 6.01 seconds, 16 players ran faster than 6.5 seconds, and all 18 players ran faster than 7.01 seconds. Let’s compare that to our first cumulative frequency table.