# Question Video: Estimating the Mode for a Grouped Data Set Mathematics

The table represents the time taken by some people to travel to work. Calculate an estimation for the modal number of minutes the people take to travel to work.

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### Video Transcript

The table represents the time taken by some people to travel to work. Calculate an estimation for the modal number of minutes the people take to travel to work.

The table that we are given showing the time taken for people to travel to work is in the form of a grouped frequency table. For example, 10 people take a time of 4.5 minutes or more up to but not including 9.5 minutes to get to work. We are asked to calculate an estimate for the mode, and the mode is the most common value or values. It’s not possible to extract the mode from a grouped data set. The only thing we can do from a grouped frequency table is recognize the modal class, which is the class with the highest frequency. As the class 9.5 minutes or more has the highest frequency of 15, then this is the modal class.

So, from the table, we have identified the modal class, and we can further identify an estimate for the mode by drawing a histogram. There are some important points to note when drawing a histogram. When we have a histogram, we don’t have bars with spaces in between them. Instead, we have a continuous 𝑥-axis representing the variable, which will be time in minutes here. The rectangular bars representing the frequencies have their vertical line segments on the upper and lower boundaries of each class.

So, once we have our histogram, we identify the modal class, which is the class with the highest bar. We then draw two lines from each of the top corners of this modal class bar to the adjacent corners of the classes on each side, which will look something like this. We then draw a vertical line from the point of intersection to the 𝑥-axis. We can use the grid lines to help us identify this estimate for the mode. Therefore, we can give the answer that an estimate for the modal number of minutes the people took to travel to work is 11.5 minutes.