Question

Use the following set of data to answer the questions. $$ \begin{array}{llllll} 4.5 & 3.2 & 3.5 & 3.9 & 3.5 & 3.9 \\ 4.3 & 4.8 & 3.6 & 3.3 & 4.3 & 4.2 \\ 3.9 & 3.7 & 4.3 & 4.4 & 3.4 & 4.2 \\ 4.4 & 4.0 & 3.6 & 3.5 & 3.9 & 4.0 \end{array} $$ Draw a stem and leaf plot, using the number in the ones place as the stem.

Short answer

Question: Create a stem and leaf plot using the given set of 24 data points, with the number in the ones place as the stem. Data points: 3.2, 3.3, 3.4, 3.5, 3.5, 3.6, 3.7, 3.9, 3.9, 3.9, 4.0, 4.0, 4.2, 4.2, 4.3, 4.3, 4.4, 4.4, 4.5, 4.8 Answer: Stem and leaf plot for the given data: ``` Stem | Leaf ------------- 3 | 2 3 4 5 5 6 7 9 9 9 4 | 0 0 2 2 3 3 4 4 5 8 ```

Step-by-step solution

Identify the stems

Using the number in the ones place as the stem, we have the following stems: 3, 4. We will group the numbers based on these stems.

Separate the values and arrange within each group

Now, we separate the data according to the stems and arrange them in ascending order within each group: - Stem 3: 3.2, 3.3, 3.4, 3.5, 3.5, 3.6, 3.7, 3.9, 3.9, 3.9 - Stem 4: 4.0, 4.0, 4.2, 4.2, 4.3, 4.3, 4.4, 4.4, 4.5, 4.8

Create the stem and leaf plot

Finally, we create the stem and leaf plot as follows: ``` Stem | Leaf ------------- 3 | 2 3 4 5 5 6 7 9 9 9 4 | 0 0 2 2 3 3 4 4 5 8 ``` The stem and leaf plot is now complete.

Key concepts

Data Visualization

Data visualization is a critical aspect of understanding complex datasets in an intuitive and clear manner. A stem and leaf plot is an excellent example of this process, transforming numerical data into a graphical format that is easy to digest. In the context of educational content, consider this plot as a way to visualize a ranked order of numbers, where the 'stem' represents the leading digit(s) and the 'leaf' represents the trailing digit(s).

The benefit of such a plot is that it maintains the original data values while also offering a visual display of the data structure. For students, the added advantage is recognizing patterns, such as the distribution of data or the presence of any outliers. It functions similarly to a histogram but is more specific, showing individual data points.

Converting the group of numbers from our exercise into a stem and leaf plot allows for immediate visual feedback on the range, central tendency, and frequency of data points, providing a comprehensive picture that purely numerical data can lack.

Descriptive Statistics

Descriptive statistics give us the ability to summarize and describe the main features of a dataset beautifully. A stem and leaf plot offers a form of descriptive statistic by organizing data in a way that conveys information quickly and accurately. The plot informs us not only about the individual values but also how frequently they occur, which is essential for the understanding of data.

Through descriptive statistics, students can grasp concepts such as mean, median, mode, range, and variance—all necessary for data interpretation. In our exercise, for instance, the stem represents the 10th place of the values, and leaves show their 1st place. Therefore, it illustrates the frequency of numbers within particular ranges, enabling the viewer to assess the dataset's characteristics at a glance. This simplification aids in immediate comprehension and provides a strong foundation for further statistical analysis.

Frequency Distribution

Frequency distribution is the backbone of many statistical analyses, depicting how often each value in a set of data occurs. In simpler terms, it shows the frequencies of different outcomes in a sample. A stem and leaf plot is a visual representation of frequency distribution that is compact and precise, exhibiting each data point's frequency directly.

When creating a stem and leaf plot, as we did in our exercise, you effectively sort the numerical data into 'bins' based on the stems (the 10s place). As seen, the leaves (the 1s place) are then listed, giving a straightforward indication of how many times each stem-leaf combination appears. This method provides a transparent overview of the distribution of data, highlighting the concentration of values, and it is particularly useful for identifying patterns and anomalies within the dataset.

Understanding frequency distribution through this method assists students in gaining insight into the nature of the dataset—information that is invaluable for further statistical study and real-world problem-solving.