Question Video: Stem-and-leaf plot-Bugs Mathematics

A class of students were asked to count and record the number of bugs that they could find in their yards in 30 minutes. The results were as follows: 21, 35, 42, 11, 13, 77, 14, 17, 31, 27, 15, 53, 12, 25, 31, 18, 22, 16, 72, 14, 91, 34, 19, 23. i) Write the stems in ascending order, of a stem-and-leaf plot for the data. ii) Display the data in a stem-and-leaf plot. iii) Use your stem-and-leaf plot to find out how many students counted bugs in their yards.

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Video Transcript

A class of students were asked to count and record the number of bugs that they could find in their yards in 30 minutes. The results were as follows: 21, 35, 42, 11, 13, 77, 14, 17, 31, 27, 15, 53, 12, 25, 31, 18, 22, 16, 72, 14, 91, 34, 19, 23. Write the stems, in ascending order, of a stem-and-leaf plot for the data. Display the data in a stem-and-leaf plot. Use your stem-and-leaf plot to find out how many students counted bugs in their yards.

We can see the list of values here, which begins with the value of 21 that would indicate that one student had found 21 different bugs in their yard. What we’re asked to do is to take this list of numerical values and put it into a stem-and-leaf plot. A stem-and-leaf plot is a special type of table where the leaves of each number will represent the final digit of each number. As all of the values here are two-digit numbers, then the leaves will all be the values in the ones column and the stem will be the value in the tens column.

For example, the stem of the first number would be two, the second stem would be three, the third stem would be four, and so on. Notice that a number of these stems will have duplicates. For example, there’s a number 11 and a number 13, which indicates that there’ll be two values that have a stem of one. The best way perhaps to write the stems in ascending order is to start by creating our stem-and-leaf plot. The smallest value that we have is 11, and the largest value is 91. Therefore, our stems will need to go from one to nine.

So here we have the stems written. We can include the stem of zero if we wish, although it’s not essential. As we go through to creating the stem-and-leaf plot, we’ll also need to include a key. We can choose any value to represent the key. Here, I’ve chosen a value with a stem of one and a leaf of two to indicate that that means 12 bugs. So that would be the first part of the question answered. The stems are written in ascending order.

We’ll now begin to answer the second question, which is where we fill in the data values into the stem-and-leaf plot. Because we have a large data set here, we can begin by filling in the values so that the leaves are given in an unordered way. Once we have all of the values into the stem-and-leaf plot, then we’ll rewrite it so that the leaves are in order. So let’s take the first value of 21. This will have a stem of two and a leaf of one. The second value of 35 has a stem of three and a leaf of five.

We can input the next two values of 42 and 11. But notice that when it comes to the value of 13, we need to put a comma and then the leaf of three. We can continue until all the values are in the stem-and-leaf plot. We can notice, for example, that the value of 31 occurred twice, but we must still write it into our stem-and-leaf plot twice. We’ll now put the leaves in each stem into ascending order. Having the leaves in order also allows us to interpret the data and draw any conclusions we may want to. And so that’s our answer for the second part of the question. Here’s a fully complete and ordered stem-and-leaf diagram along with the key.

The third part of this question asks us to find out how many students counted bugs in their yards from the stem-and-leaf plot. In order to do this, we need to count the total number of leaves. In the first row, we have 10 different leaves, then five leaves, four, one, one, two, and one. Adding these all together would give us the value of 24. So our answer would be that 24 students counted bugs in their yards. It’s also a very good check as we’re completing the stem-and-leaf diagram to make sure that we’ve got all of the values in. If we’d counted each individual data value that we were originally given, we would also find that there were 24 different data values.

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