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Interpret Stem and Leaf Plots Calculator

Interpret Stem and Leaf Plots Calculator

Interpret Stem and Leaf Plots Calculator

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A stem and leaf plot is a unified way of visualizing the financial information using a single graph. It plots certain yearly dataset, like profit, funds, or expenses. Each item might appear on the x-axis or y-axis, depending on how its being plotted. We’re displaying this graph so you can see how it’s done. Changes in the color of the line across each axis illustrates the change over time.

Plot

A statistician for a basketball team tracked the number of points that each of the 12 players on the team had in one game. And then made a stem-and-leaf plot to show the data. And sometimes it's called a stem-plot. How many points did the team score? And when you first look at this plot right over here, it seems a little hard to understand. Understand we have 0, 1, 2 under leaf you have all of these digits here. How does this relate to the number of points each student, or each player, actually scored? And the way to interpret a stem-and-leaf plot is the leafs contain-- at least the way that this statistician used it-- the leaf contains the smallest digit, or the ones digit, in the number of points that each player scored. And the stem contains the tens digits. And usually the leaf will contain the rightmost digit, or the ones digit, and then the stem will contain all of the other digits. And what's useful about this is it gives kind of a distribution of where the players were. You see that most of the players scored points that started with a 0. Then a few more scored points that started with a 1. And then only one score scored points to started with a 2, and it was actually 20 points. So I'm going to actually write down all of this data in a way that maybe you're a little bit more used to understanding it. So I'm going to write the 0's in purple. So there's, let's see, 1, 2, 3, 4, 5, 6, 7 players had 0 as the first digit. So 1, 2, 3, 4, 5, 6, 7. I wrote seven 0's. And then this player also had a 0 in his ones digit. This player, I'm going to try to do all the colors, this player also had a 0 in his ones digit. This player right here had a 2 in his ones digit, so he scored a total of 2 points. This player, let me do orange, this player had 4 for his ones digit. This player had 7 for his ones digit. Then this player had 7 for his ones digit. And then, let me see, I'm almost using all the colors, this player had 9 for his ones digit. So the way to read this is, you had one player with 0 points. 0, 2, 4, 7, 9 and 9. But you can see, and it's kind of silly saying the zero was a tens digit, you could have even put a blank there. But the 0 lets us know that they didn't score anything in the tens place. But these are the actual scores for those seven players. Now let's go to the next row in the stem-and-leaf plot. So over here, all of the digits start with, or all of the points start with 1, for each of the players. And there's four of them. So 1, 1, 1, and 1. And then we have this player over here, his ones digit, or her ones digit, is a 1. So this player, this represents 11. 1 in the tens place, 1 in the ones place. This player over here also got 11. 1 in the tens place, 1 in the ones place. This player, let me do orange, this player has 3 in the ones place. So he or she scored 13 points. 1 in the tens place, 3 in the ones place. 13 points. And then I will do this in purple. This player has 8 in their ones place. So he or she scored 18 points. 1 in the tens place, 8 in the ones place. 18 points. And then finally, you have this player that has the tens digit is a 2. And then the ones digit is a 0. I'll circle that in yellow. It is a 0. So he or she scored 20 points. So looking at the stem-and-leaf plot, we were able to extract out all of the number of points that all of the players scored. And once again, what was useful about this, is you see how many players scored between 0 and 9 points, including 9 points. How many scored between 10 and 19 points, and then how many scored 20 points or over. And you see the distribution right over here. But let's actually answer the question that they're asking us to answer. How many points did the team score? So here we just have to add up all of these numbers right over here. So we're going to add up, I'll start with the largest, so 20 plus 18 plus 13 plus 11 plus 11-- 13, 11, 11-- plus 9 plus 7 plus 7 again plus 4 plus 2. Did I do that right? We have two 11's, then a 9, then two 7's, then a 4 then a 2, and then these two characters didn't score anything. So let's add up all of these together. So 0 plus 8 is 8, plus 3 is 11, plus 1 is 12, plus 1 is 13, plus 9 is 22, plus 7 is 27, 34, 38, 40. So that gets us to 40. Let me do that one more time. 8, 11, 11, 12, 13, 22, 29, 29, and then 29, 36, 40, and 42. Looks like I actually might have messed-- let me do that one more time. This is the hardest part, adding these up. So let me try that one last time. I'm just going to state where my sum is. So 0, 8, add 3, 11, 12, 13, 22, 29, 36, 40, 42. So it's a good thing that I double checked that. I made a mistake the first time. 4 plus 2 is 6, 7, 8, 9, 10. So we get to 102 points. The team, in total, scored 102 points.

Stem and leaf plots are a great way to visually see what age groups are at the party. What is even better, is that after you get the quick visual, you have the actual values in the plot to work with as well. (Source: www.softschools.com)

Value

The counts are in the first column on the left. The count for the row that contains the median value is enclosed in parentheses. The values for rows above and below the median are cumulative. The count for a row above the median represents the total count for that row and all the rows above it. The value for a row below the median represents the total count for that row and all the rows below it. The downside of frequency distribution tables and histograms is that, while the frequency of each class is easy to see, the original data points have been lost. You can tell, for instance, that there must have been three listed values that were in the forties, but there is no way to tell from the table or from the histogram what those values might have been.

The "stem" is the left-hand column which contains the tens digits. The "leaves" are the lists in the right-hand column, showing all the ones digits for each of the tens, twenties, thirties, and forties. As you can see, the original values can still be determined; you can tell, from that bottom leaf, that the three values in the forties were 40, 40, and 41. (Source: www.purplemath.com)

Example

For example, a manager at a bank collects wait time data and creates a simple stem-and-leaf plot. The stem-and-leaf plot appears to have two peaks. Upon further investigation, the manager determines that the wait times for customers who are cashing checks is shorter than the wait time for customers who are applying for home equity loans. The manager adds a group variable for customer task, and then creates a stem-and-leaf plot with groups. The stem-and-leaf plot with groups shows that the peaks correspond to the two groups.The numbers are arranged by place value. The largest place-value digits are placed in the stem. Stemplots in the real world aren’t usually labeled with the place-values that the stem represents — it’s usually up to you to figure it out based on the context and the data. However, in textbooks and other education materials it’s common for stemplots to be labeled. For example, a key next to the following stemplot tells you that 7|5 means 75, indicating that the stem represents tens and the leaf represents units.

Now, back to that first column of numbers appearing in Minitab's plot. That column contains what are called depths. The depths are the frequencies accumulated from the top of the plot and the bottom of the plot until they converge in the middle. For example, the first number in the depths column is a 1. It comes from the fact that there is just one number in the first (6) stem. The second number in the depths column is also a 1. It comes from the fact that there is 1 leaf in the first (6) stem and 0 leaves in the second (the first 7) stem, and so 1 + 0 = 1. The third number in the depths column is a 3. It comes from the fact that there is 1 leaf in the first (6) stem, 0 leaves in the second (the first 7) stem, and 2 leaves in the third (the second 7) stem, and so 1 + 0 + 2 = 3. Minitab continues accumulating numbers down the column until it reaches 32 in the last 9 stem. Then, Minitab starts accumulating from the bottom of the plot. The 5 in the depths column comes, for example, from the fact that there is 1 leaf in the last (14) stem, 1 leaf in the second 13 stem, 0 leaves in the first 13 stem, 1 leaf in the second 12 stem, and 2 leaves in the first 12 stem, and so 1 + 1+ 0 + 1 + 2 = 5. (Source: online.stat.psu.edu

Set

The basic idea behind a stem-and-leaf plot is to divide each data point into a stem and a leaf. We could divide our first data point, 111, for example, into a stem of 11 and a leaf of 1. We could divide 85 into a stem of 8 and a leaf of 5. We could divide 83 into a stem of 8 and a leaf of 3. And so on. To create the plot then, we first create a column of numbers containing the ordered stems. Our IQ data set produces stems 6, 7, 8, 9, 10, 11, 12, 13, and 14. Once the column of stems are written down, we work our way through each number in the data set, and write its leaf in the row headed by its stem. 6-9 Stem-and-Leaf Plots LESSON Complete each activity and answer the questions. 1. Use the data in the table to complete the stem-and-leaf plot below. Find each value of the data set. 2. smallest value 3. largest value 4. mean 5. median 6. mode 7. range 37 82 82 79.4 98 61 Stem Leaves 61 4 71 6 82 2 9018 Key: 6 | 5 65 Stem Leaves 37 9 40 8

Draw a stem-and-leaf plot for each data set. 3) Name Age Name Age Name Age Rudolf Ludwig Mössbauer 32 Stanley Ben Prusiner 55 Robert Merton Solow 63 Wolfgang Ketterle 44 Torsten Nils Wiesel 57 Stanley Cohen 64 Joseph Leonard Goldstein 45 Richard Axel 58 Peter Mansfield 70 Aung San Suu Kyi 46 Robert Coleman Richards 59 Vernon Lomax Smith 75Represent single or multiple data sets with dot plots, histograms, stem plots (stem and leaf), and box plots. • A1.S.ID.A.2 . Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. • A1.S.ID.A.3 (Source: 5y1.or

 

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