A survey was done to collect data on the number of hours per month that students in a class spent doing three activities: (1) playing computer games, (2) watching TV, and (3) playing sports. The data was put into three stem-and-leaf plots, as shown below. How many students played computer games for more than 60 hours a month? What were the greatest and least numbers of hours a student played sports for? Comparing the stem-and-leaf diagrams for computer games and watching TV, what can you say about the number of hours students spent on these two activities?
A stem-and-leaf plot is a special table where each data value is split into a stem and a leaf. In this question, we are given three different stem-and-leaf plots: one on computer games, one on watching TV, and one on playing sports. We’ll need to use the key to help us interpret the data. For example, if we look at the stem-and-leaf plot on computer games and we look at this value two with a stem of one, that means the value 12 or 12 hours. It means that one student spent 12 hours in the month playing computer games. The value underneath of four represents 24 hours playing computer games. Notice that this is different to the four in the row below, as the second four has a stem of three, so that represents 34 hours.
So let’s have a look at the first question, how many students played computer games for more than 60 hours a month? In order to answer this, we just need to look at the first stem-and-leaf plot on computer games. To find the number of students who played for more than 60 hours a month, that means we’ll need to consider all the values that have a stem of six or higher. Remember that each leaf represents a student, so we’ll need to count all the individual leaves even when they’re duplicated. For example, there are three leaves of five, but that means that three students played computer games for 75 hours. There are five leaves that have a stem of six and seven leaves with a stem of seven. Adding five and seven gives us 12, so the answer for the first question is that there are 12 students who played computer games for more than 60 hours a month.
Let’s have a look at the second question, what were the greatest and least numbers of hours a student played sports for? To answer this, we’ll need to consider the third stem-and-leaf plot. Finding the greatest and least numbers in a stem-and-leaf plot is relatively simple as stem-and-leaf plots are usually given in order. The greatest value will be given by the last leaf in the stem-and-leaf plot, which here is a zero. But remember that we need to consider the stem, so the last leaf represents 50. The first leaf is also a zero with a stem of zero. So that means that a student played zero hours of sport in the month. We can therefore give the answer for this part that the least number of hours would be zero hours per month and the greatest would be 50 hours per month.
Let’s have a look at the final part of this question, comparing the stem-and-leaf diagrams for computer games and watching TV, what can you say about the number of hours students spent on these two activities? Here, we’ll need to compare two different stem-and-leaf plots. When we’re given a statement for a question like this, we want to give an idea of the general pattern, but we also want to use some specific values to illustrate this pattern. For example, if we look at the stem-and-leaf plot for computer games, we might notice that there’s a lot of high values here. But if we just wrote the statement, “lots of students play a high number of hours of computer games a month,” it might be true, but it’s not sufficient.
If we count the number of leaves in each of these stem-and-leaf plots, there’s actually 22. That will give us some help when we compare the values. There are 15 out of these 22 students who play computer games for more than 50 hours a month, so that’s quite a high majority of the students. It’s also worth commenting on the very small number of leaves we have at the start of this stem-and-leaf plot. Very few students are actually playing computer games for less than 30 hours per week. It’s less than 30 as these stems go up to a stem of two. We can remove the sports stem-and leaf-plot so we can have somewhere to write the answer. We could write a statement such as “Very few students played computer games for less than 30 hours per month, and the vast majority played for more than 50 hours.”
Let’s see what we can say about the number of hours spent watching TV. One of the things we might notice about this stem-and-leaf plot is there’s actually quite a lot of leaves or students at the start of this stem-and-leaf plot. Students appear to spend fewer hours watching TV than they do playing computer games per month. A good statement to write might be most students watch TV for less than 30 hours per month. And so we could give our completed answer with the statements on each stem-and-leaf plot. It’s worth pointing out that, of course, there are a range of different answers that would be equally valid. But we’ve given an idea of a pattern of the hours spent doing each activity alongside specific values, for example, 30 hours or 50 hours per month.