 In this video, we're going to look at a way of presenting data, the histogram. There are lots of misconceptions about histograms, and we will try and clear up some of these along the way. Consider this frequency table of data. You might be tempted to plot the information in a bar chart. However, if you did, it would end up looking like this. At first glance, this might look perfectly fine, but there are actually a couple of issues with it. Firstly, the data in our table is continuous, meaning that there is a group for every value, including non-integers within the range of 100 and 200. Bar charts are not used for continuous data because they require gaps between the bars and gaps don't work for continuous values. The second problem is that the group 150 to 160 has the same height as 120 to 140, even though it represents a smaller range. This therefore does not give us a true comparison of the data. To solve these issues, we use something called frequency density. Because plotting against frequency doesn't work when the group sizes, also known as class widths, are different, we plot against the frequency density instead. We calculate frequency density by dividing the frequency of each group by the size of the group. As density is a measure of how much mass there is in a volume, frequency density is a measure of frequency in a set space. This allows us to solve the problem with unfair comparisons as all values plotted will have their group size accounted for. We start by adding an additional column titled frequency density. We then divide each frequency value by its corresponding class width to find the frequency density. Pause the video and see if you can work out the frequency density for these values. Let's see how you did. The first frequency value is 20, which divided by a class width of 20, gives us a frequency density of 1. The remaining values are found like this. We can take these values and plot them against frequency density, not frequency. If you want to try this yourself, pause now. The completed histogram should look like this. The bars touch on a histogram, which works with our continuous data, and we can draw clear conclusions about what the data shows now. As we can see, now the group 150 to 160 is taller than the 120 to 140, showing a higher frequency for the same class width. It's also important to be able to interpret the data in a given histogram. Take a look at this one here. Estimate the number of people who took between 30 and 90 seconds to complete the test. If you want to have a go first, pause the video now. Firstly, we need to rearrange our histogram equation to find frequency. Because frequency density is equal to the frequency divided by the class width, to find frequency alone, we have to multiply the class width by the frequency density. If we look at our histogram, we plot frequency density against class width, so the area of each bar is the same as its frequency. Rectangle 1 has a height of 0.5 and a width of 30, because the bar's width is 30 seconds to 60 seconds. Between these tells us there are 15 people in rectangle 1 between 30 and 60 seconds. Rectangle 2 has a height of 1.5 and also a width of 30 seconds, from 60 seconds to 90 seconds. 1.5 multiplied by 30 equals 45 people, so in total there are 15 plus 45, giving an estimate of 60 people. Have a go at this question. Estimate the number of people whose average speed was 10 to 40 miles per hour. Rectangle 1 has a width of 10 between 10 seconds and 20 seconds, a frequency density of 2, so 20 people in total. Rectangle 2 has a width of 20, from 20 to 40, and a frequency density of 6, so 120 people in total. There are therefore as an estimate 140 people whose average speed was in the range of 10 to 40 miles per hour. It's important to remember that when you have different class widths, you need to plot frequency density on the y-axis. You can however have a histogram with frequency, but the class widths must be even. These tend to feature discrete data, such as shoe sizes and scores, rather than continuous values.