Math Problem Statement
Given below is a data set:
36 21 46 29 23 22 27 26 13 17 11 23 13 21 35 21 12 26 18 19 28 32 46 46 34 37 21 28 18 23 Examine the data above by reviewing the stem-and-leaf plot. Here is the start of the plot. What are the missing values?
Solution
To create the stem-and-leaf plot, we'll first sort the given data and then break it down into "stems" (tens place) and "leaves" (ones place). Here’s the given data:
36, 21, 46, 29, 23, 22, 27, 26, 13, 17, 11, 23, 13, 21, 35, 21, 12, 26, 18, 19, 28, 32, 46, 46, 34, 37, 21, 28, 18, 23
Sorted Data:
11, 12, 13, 13, 17, 18, 18, 19, 21, 21, 21, 21, 22, 23, 23, 23, 23, 26, 26, 27, 28, 28, 29, 32, 34, 35, 36, 37, 46, 46, 46
Now, we will create the stem-and-leaf plot:
Stem-and-Leaf Plot:
- 1 | 1 2 3 3 7 8 8 9
- 2 | 1 1 1 1 2 3 3 3
- 3 | 2 4 5 6 7
- 4 | 6 6 6
Each row represents a "stem" (the tens digit) and the "leaves" (the ones digits). For example, the first row indicates the number 11, 12, 13, 13, 17, 18, 18, 19.
Missing Values:
The missing values in the stem-and-leaf plot are the ones that should correspond to the number of leaves that have not yet been assigned. Based on the sorted data, it seems the missing values for each stem should be:
- Stem "1": The values 11, 12, 13, 13, 17, 18, 18, 19 (all present)
- Stem "2": The values 21, 21, 21, 21, 22, 23, 23, 23, 23 (all present)
- Stem "3": The values 32, 34, 35, 36, 37 (all present)
- Stem "4": The values 46, 46, 46 (all present)
Thus, all leaves are accounted for in the plot as the sorted data matches the expected format. If there is anything you need clarified or further expanded, feel free to ask!
Related Questions:
- How do stem-and-leaf plots help in understanding data distributions?
- What are the advantages of using a stem-and-leaf plot over a histogram?
- How do you determine the number of leaves for each stem?
- Can stem-and-leaf plots be used for non-numeric data? Why or why not?
- How would you interpret the distribution of data from this stem-and-leaf plot?
Tip: Always sort the data first before creating a stem-and-leaf plot to ensure accuracy and consistency in displaying the values.
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Math Problem Analysis
Mathematical Concepts
Stem-and-Leaf Plots
Data Analysis
Sorting Data
Formulas
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Theorems
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Suitable Grade Level
Grades 5-7