3.22: Stem-and-Leaf Plots, Range of a Data Set
Remember Julie? Have you ever wondered how to calculate range?
Well, here is the stem - and- leaf plot that Julie created in the last Concept.
This Concept is all about how you can use a stem - and - leaf plot to determine the range of a set of data. Pay attention and by the end of the Concept you will know how Julie can figure out the range of the data.
Guidance
In the last Concept, you learned how to create a stem - and - leaf plot for a set of data. Once you have the stem - and - leaf plot made, you can use it to figure out the range of a set of data.
What is the range?
The range is the difference between the maximum score and the minimum score.
The smallest number in the stem-and-leaf plot is 22. You can see that by looking at the first stem and the first leaf. The greatest number is the last stem and the last leaf on the chart. In this case, the largest number is 55. To find the range, we subtract the smallest number from the largest number. This difference will give us the range.
55 - 22 = 33
The range is 33 for this set of data.
Look at the following stem-and-leaf plot and answer these questions.
Example A
What is the range for this data set?
Solution: 35
Example B
What is the smallest interval?
Solution: 12 - 14
Example C
What is the greatest interval?
Solution: 42 - 47
Now back to Julie and the stem - and - leaf plot. Here it is once again.
What is the range of Julie's data?
To figure this out, we can find the difference between the greatest value in the data set and the smallest value in the data set.
\begin{align*}86 - 52 = 34\end{align*}
The range of the data is 34.
Vocabulary
Here are the vocabulary words in this Concept.
- Stem-and-leaf plot
- a way of organizing numbers in a data set from least to greatest using place value to organize.
- Data
- information that has been collected to represent real life information
- Ascending
- from smallest to largest
- Descending
- from largest to smallest
- Interval
- a specific period or arrangement of data
- Range
- the difference from the largest value to the smallest value
Guided Practice
Here is one for you to try on your own.
What is the range of this data set?
To figure this out, we find the difference between the largest value in the data set and the smallest value in the data set.
The largest value is 68.
The smallest value is 33.
\begin{align*}68 - 33 = 35\end{align*}
The range of the data set is 35.
Video Review
Here are videos for review.
Khan Academy Stem-and-Leaf Plots
Great video on organizing, building and interpreting a stem and leaf plot.
http://www.mathplayground.com/howto_stemleaf.html
Practice
Directions: Use each stem - and - leaf plot to answer the following questions.
Stem | Leaf |
---|---|
6 | 8 |
7 | 5 7 9 |
8 | 0 2 |
9 | 2 6 6 7 |
1. What is the smallest value in the plot?
2. What is the greatest value in the plot?
3. What is the range of the data?
Stem | Leaf |
---|---|
0 | 8 |
1 | 2 7 8 9 |
2 | 2 3 |
3 | 1 5 |
4 | 0 |
4. What is the smallest value in the data set?
5. What is the greatest value in the data set?
6. What is the range of the data?
7. Name the first interval.
8. Name the second interval.
9. Name the third interval.
10. Name the fourth interval.
11. Which interval has the greatest number of values in it?
12. Which interval has the smallest number of values in it?
13. Because the 4 stem has a zero in it, does that mean that there aren't any values in it?
14. True or false. You can create a stem - and - leaf plot with a range in the hundreds?
15. True or false. You can create a stem - and - leaf plot without using intervals?
Ascending
Ascending order indicates that values are arranged from smallest to largest (to ascend means to move upward).Data
Data is information that has been collected to represent real life situations, usually in number form.Descending
A descending pattern indicates that values in the pattern are arranged from greatest to least (to descend means to move downward).Interval
An interval is a range of data in a data set.Range
The range of a data set is the difference between the smallest value and the greatest value in the data set.Stem-and-leaf plot
A stem-and-leaf plot is a way of organizing data values from least to greatest using place value. Usually, the last digit of each data value becomes the "leaf" and the other digits become the "stem".Image Attributions
Here you'll learn to use a stem - and - leaf plot to find the range of a set of data.
Concept Nodes:
Ascending
Ascending order indicates that values are arranged from smallest to largest (to ascend means to move upward).Data
Data is information that has been collected to represent real life situations, usually in number form.Descending
A descending pattern indicates that values in the pattern are arranged from greatest to least (to descend means to move downward).Interval
An interval is a range of data in a data set.Range
The range of a data set is the difference between the smallest value and the greatest value in the data set.Stem-and-leaf plot
A stem-and-leaf plot is a way of organizing data values from least to greatest using place value. Usually, the last digit of each data value becomes the "leaf" and the other digits become the "stem".