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Stem-and-Leaf Plots

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Stem-and-Leaf Plots

Have you ever seen a chimpanzee? Take a look at this dilemma.

A zoologist takes the weights of male and female chimpanzees at 1 year of age. She finds the following data, in pounds, and places it in order from smallest to largest.

Females: 14, 17, 19, 19, 20, 21, 23, 24

Males: 18, 22, 24, 25, 26, 28, 31, 32, 34

Make a double stem-and-leaf plot that represents this data so we can compare the males and the females in the same data display. Pay attention and you will know how to do this by the end of the Concept.

Guidance

Measures of central tendency are an important method for interpreting a set of data. However, humans tend to be very visual. That is, many people understand things best when they can see them. For that reason, we have a variety of tools which allow us to see a set of data. These tools include plots and graphs. Each type of visual tool has advantages and the best type of plot or graph depends on the situation. Indeed, sometimes it is a matter of preference as many different graphs could be used to illustrate the same data.

Let's think about stem-and-leaf plots.

Consider a stem and its leaves. The stem is a strong base from which the leaves sprout. This is the idea of a stem-and-leaf plot. They allow us to see groups of data and tendencies quickly while at the same time showing every single piece of data.

We organize a stem-and-leaf plot according to the largest base ten value and the smaller base ten values.

Take a look at this dilemma.

An accountant must consider the cost of healthcare for the employees at a company. The healthcare costs are based on age of the employees. She finds that the ages of the employees are as follows: 32, 19, 37, 22, 25, 46, 58, 35, 41, 45, 35, 27, 29, 42, 53, 70, 56, 34, 29, 30, 21, 24, 27, and 45.

This data is difficult to understand in an unorganized list. Measures of central tendency could be calculated but they would not help to determine healthcare costs. A stem-and-leaf plot will give her a better idea of numbers of employees per age group.

To create a stem-and-leaf plot, we first must put the data in order from smallest to largest:

19, 21, 22, 24, 25, 27, 27, 29, 29, 30, 32, 34, 35, 35, 37, 41, 42, 45, 45, 46, 53, 56, 58, 70.

Now, choose stem values. That means to choose values that would be the first digit(s) of appropriate groupings. In this case, because our youngest employee is 19 and the oldest is 70, we can use the tens place as our stem. We construct the stem vertically, then, as shown below. Then, we place each piece of data, the leaves, in the plot, next to its stem. We place the leaves in order, only separated by a column. The stem, the tens place, is not repeated.

&\text{Stem} \quad \text{Leaves}\\& \quad \ \begin{array}{c|c c c c c c c c} 1 & 9 \\2 & 1, & 2, & 4, & 5, & 7, & 7, & 9, & 9\\3 & 0, & 2, & 4, & 5, &	5, & 7 \\4 & 1, & 2, & 5, & 5, &	6 \\5 & 3, & 6, & 8 \\6 \\7 & 0 \\\end{array}

The stem-and-leaf plot is complete.

Now, look at the plot. What trends can you see?

The bulk of the employees are in their 20’s and 30’s. By counting off, you can quickly locate the median. You may also notice the importance of lining up the numbers in columns so that you can quickly see how many data items there are per row.

If our situation had used numbers in the hundreds, then the hundreds would have become the largest stem. If it had been in the thousands, then the thousands would have been the largest stem. You get the idea!

If we had been given two sets of data, then we could have made a double stem-and-leaf plot!

Use this data set to answer the following questions.

{22, 23, 24, 25, 33, 34, 40, 51, 52, 52, 60, 61, 62}

Example A

Which stem would have the most leaves?

Solution: 20's

Example B

Would you use stems in the ones or tens?

Solution: Tens

Example C

Which stem would have the least leaves?

Solution: 40's

Now let's go back to the dilemma from the beginning of the Concept.

& \quad \text{Females} \qquad \qquad \quad \text{Males}\\& \begin{array}{c c c c|c|c c c c c c} 9, & 9, & 7, & 4 & 1 & 8 \\4, & 3, & 1, & 0 & 2 & 2, & 4, & 5, & 6, & 8 \\& & & & 3 & 1, & 2, & 4 \\\end{array}

In this plot, the female data on the left begins with smallest data closest to the stem and increases as you go left. You can see from the stem-and-leaf plot that the tendency is for the males to weigh more than the females after a year. We can also see that there are more males in this group than females.

Vocabulary

Stem-and-Leaf Plots
a visual display of data that takes the largest base ten of a value and separates it by large bases and smaller values in the data.
Double Stem-and-Leaf Plots
Stem-and-leaf plots that show two different sets of data on the same display by organizing according to stems and leaves of base ten values.

Guided Practice

Here is one for you to try on your own.

Create a stem-and-leaf plot of the mass of geodes found at a volcanic site. Scientists measured 24 geodes in kilograms and got the following data: .8, .9, 1.1, 1.1, 1.2, 1.5, 1.5, 1.6, 1.7, 1.7, 1.7, 1.9, 2.0, 2.3, 5.3, 6.8, 7.5, 9.6, 10.5, 11.2, 12.0, 17.6, 23.9, 26.8.

Solution

Now we need to build a stem-and-leaf plot. We can begin by organizing the data.

The stem for this plot could be either the ones place or the tens place. If we use the ones place, it would require 24 rows. That’s too many to be useful. We should, then, use the tens place.

\begin{array}{c|c c c c c c c c c c c c c c c c c c c} 0 & .8, & .9, & 1.1, & 1.1, & 1.2, & 1.5, & 1.6, & 1.7, & 1.7, & 1.7, & 1.9, & 2.0, & 2.3, & 5.3, & 6.8, & 7.5, & 9.6, \\1 & 0.5, & 1.2, & 2.0, & 7.6, \\2 & 3.9, & 6.8 \\\end{array}

The stem-and-leaf plot is complete.

Video Review

Stem-and-Leaf Plots

Practice

Directions: Use each situation to answer the following questions.

Students spent the following total minutes on homework last Thursday evening: 45, 45, 40, 43, 36, 50, 60, 55, 55, 45, 60, 63, 90, 75, 80

  1. Make a stem-and-leaf plot that represents the data.
  2. Which stem has the greatest number of values?
  3. Which stem has the least number of values?
  4. What can you interpret from the plot?
  5. Explain the intervals that you chose.
  6. Why is it necessary to show intervals for which there was no data?

A hybrid car and a gasoline-only car filled up on the same days of the month. The drivers recorded the gasoline costs for the two cars.

Hybrid: $17, $24, $19, $21, $10, $12, $15, $20, $6, $16

Gasoline-Only: $34, $27, $15, $31, $29, $27, $24, $14, $35, $28

  1. Create a double stem-and-leaf plot to represent this data.
  2. Which stem has the greatest number of values for a hybrid?
  3. Which stem has the greatest number of values for a gasoline-only car?
  4. What can you conclude from your stem-and-leaf plot?

Kelly earned the following amounts of money babysitting: $30.00, $10.00, $15.00, $20.00, $18.00, $22.00, $35.00, $40.00 and $58.00.

  1. Make a stem-and-leaf plot that represents the data.
  2. Which stem has the greatest number of values?
  3. Which stem has the least number of values?
  4. What can you interpret from the plot?
  5. What was the median amount of money that she made?

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