 In this video, we are going to look at how we can find the mean from data in a table. A mean is commonly associated with the term average and is found by dividing the sum total of values by the number of values themselves. The easiest mean questions involve simply adding given data and dividing by the total such as this question here. Finding the mean from a frequency table takes a little more consideration than finding the mean from a basic list of data. Consider this frequency table, showing the data for points scored in a game. By understanding that the frequency says that score 1 occurred 2 times, score 2 occurred 5 times, etc., we can imagine the data forming a list like this. We can then simply add and divide by the number of values. However, this method will become 2 time consuming with larger quantities, so we can add 2 additional parts to our initial frequency table. The first addition is a column to the right, which we label fx. fx stands for the frequency f multiplied by the value x. In this case, points scored. By adding this, we are speeding up the process of collecting values. The second addition is a total column. We still require the total points scored divided by the total count to find the mean, and having these columns helps us to keep track of this. Have a look at this frequency table, showing the number of pets people have. We have included the fx and total columns for you. Pause the video and have a go calculating the mean. Let's see how you did. To find the fx values, we need to multiply our number of pets, x, by the frequency f. That should give you these values. We can then complete our totals. We can then divide the total pets by total frequency. In this case, the people in the survey, to get the mean value, 1.95. You may also need to be able to find the mean of data from frequency tables which look like this. This data shows the lengths of carrots to the nearest millimetre. As you can see this data has no specific value, it is grouped data shown in intervals. We cannot calculate an exact mean value from this. Any mean we calculate will therefore be an estimate. To calculate the mean of grouped data, the first step is to add the fx column, the totals and an additional column labeled midpoint. We then determine the midpoint of each interval or class. We then treat these midpoints as x and multiply them by their given frequency. The sum of the products are then divided by the total number of the values or be an estimated value of the mean. Pause here and see if you can figure out the mean. Let's see how you got on. Firstly, let's put in the midpoints. We can find these by adding the two limiting values together and dividing by two. So the first midpoint is 147. We then calculate fx by multiplying the frequency by its midpoint. The sum of fx is the total lengths of the carrots, if they were placed end to end. To find the mean length, we need to divide the sum by the total number of carrots, the frequency. This gives us a mean carrot length, 166.78mm, rounded to two decimal places. One final thing for us to consider is that the intervals from grouped data may also look like an inequality, like this. You would still find the midpoint in exactly the same way as before, but be aware that the groups may not always be the same size. If you liked the video, give it a thumbs up and don't forget to subscribe, comment below if you have any questions. Why not check out our Fuse school app as well. Until next time.