Why is the stem-and-leaf plot misleading?…

Mathematics Questions
Short Answer
Step by Step Solution
Mathematics Questions

HURRY PLS The stem-and-leaf plot below shows the amount of tips received by the servers in a restaurant in one night. A stem and leaf plot is shown. The stems from top to bottom are 0, 1, 2, 3, 5. The first column of leaves is 9, 2, 3, 1, 9. The second column of leaves is blank, 4, 6, 2, blank. The third column of leaves is blank 7, 6, 2, blank. The fourth column of leaves is blank, blank, 8, 4, blank. The fifth column of leaves is blank, blank, blank, 5, blank. Why is the plot misleading? The plot shows that the data is skewed. There is not an equal number of data points for each stem. The plot shows duplicate data points. The stem does not clearly show the outlier.

Short Answer

The analysis of the stem and leaf plot reveals missing data, specifically the absence of the stem “4,” which obscures crucial points and affects data interpretation. Furthermore, improper arrangement of leaves can misrepresent outliers, leading to a flawed understanding of the data distribution.

Step-by-Step Solution

Step 1: Analyze the Stem and Leaf Plot

Begin by examining the given stem and leaf plot where the numbers are categorized. In this case, the plot consists of stems and leaves, such as:

  • 0 | 9, 2, 3, 1, 9
  • 1 | 4, 6
  • 2 | 7, 6
  • 3 | 8, 45
  • 4 | 5

It’s critical to notice that the stem “4” is absent from the representation, losing valuable information about the data distribution.

Step 2: Identify the Missing Data

Acknowledge the implications of having a missing stem. In the plot, the absence of the stem “4” means that the corresponding leaves that should be listed next to it are not visible. Visitors can miss essential data points, making it hard to interpret the data accurately. Understanding how this omission can skew the overall picture is crucial.

Step 3: Evaluate the Misleading Nature

Recognize that the arrangement of leaves impacts clarity in the plot. When they are not sorted properly, it misrepresents the data, particularly concerning outliers. In conclusion, without a clear stem representation, the plot fails to showcase outliers, confirming the statement that “The stem does not clearly show the outlier.” This becomes an essential aspect when utilizing stem and leaf plots for data analysis.

Related Concepts

Stem And Leaf Plot

A graphical representation of data that displays the frequency of numbers in a dataset by organizing them into “stems” (the leading digit[s]) and “leaves” (the trailing digit[s])

Missing Data

Data that is not represented or is absent from a dataset, which can lead to incomplete or misleading interpretations of the data’s overall distribution

Outliers

Data points that differ significantly from other observations in a dataset, which can indicate variability or errors in the data and may affect the results of statistical analysis.

Table Of Contents
  1. HURRY PLS The stem-and-leaf plot below shows the amount of tips received by the servers in a restaurant in one night. A stem and leaf plot is shown. The stems from top to bottom are 0, 1, 2, 3, 5. The first column of leaves is 9, 2, 3, 1, 9. The second column of leaves is blank, 4, 6, 2, blank. The third column of leaves is blank 7, 6, 2, blank. The fourth column of leaves is blank, blank, 8, 4, blank. The fifth column of leaves is blank, blank, blank, 5, blank. Why is the plot misleading? The plot shows that the data is skewed. There is not an equal number of data points for each stem. The plot shows duplicate data points. The stem does not clearly show the outlier.

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