Let's break down the problem and solve it step by step.

Step 1: Organizing the Data

We are given the following set of data:

24, 36, 42, 55, 61, 48, 35, 47, 59, 63, 29, 33, 57, 50, 41, 68, 39, 45, 52, 66.

Step 1a: Sorting the Data

To create a stem-and-leaf plot, we first need to organize the data in ascending order:

Ordered Data:
24, 29, 33, 35, 36, 39, 41, 42, 45, 47, 48, 50, 52, 55, 57, 59, 61, 63, 66, 68.

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Step 2: Constructing the Stem-and-Leaf Plot

In a stem-and-leaf plot, the "stem" represents the tens digit, and the "leaf" represents the ones digit.

Stem-and-Leaf Plot Structure:

• The stem consists of the tens digits.
• The leaf consists of the ones digits.

Let’s break it down for the data:

Stem: 2, 3, 4, 5, 6
Leaves: Corresponding to the ones digits of each number.

We now group the data by the tens digit and list the ones digits:

• 2: 24
• 3: 29, 33, 35, 36, 39
• 4: 41, 42, 45, 47, 48
• 5: 50, 52, 55, 57, 59
• 6: 61, 63, 66, 68

Now, we can represent this as a stem-and-leaf plot.

Stem-and-Leaf Plot:

Stem | Leaf
--------------
  2  | 4
  3  | 9 3 5 6 9
  4  | 1 2 5 7 8
  5  | 0 2 5 7 9
  6  | 1 3 6 8

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Step 3: Describing the Distribution

Now that we have the stem-and-leaf plot, let's describe the distribution of the data.

Symmetry or Skewness

• The data is somewhat evenly distributed on both sides of the middle.
• There are no extreme outliers on either side, and the distribution is approximately symmetrical.
• While there is a slight cluster of values around the 50s (50-59), it’s not enough to skew the data significantly in one direction.

So, the distribution of the data appears symmetrical.

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Final Answer:

(a) The ordered stem-and-leaf plot is:

Stem | Leaf
--------------
  2  | 4
  3  | 9 3 5 6 9
  4  | 1 2 5 7 8
  5  | 0 2 5 7 9
  6  | 1 3 6 8

(b) The distribution of the data is approximately symmetrical.

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Would you like a more detailed explanation or help with any specific part? Feel free to ask!

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Further Questions:

1. What are the advantages of using a stem-and-leaf plot over a histogram?
2. How can we calculate the mean and median from the stem-and-leaf plot?
3. How would you modify the stem-and-leaf plot if there were more data points?
4. What can we infer about the spread of the data based on the plot?
5. Can you explain how to identify outliers using a stem-and-leaf plot?

Tip: A stem-and-leaf plot is especially helpful for small datasets as it retains the original data while giving you an immediate visual impression of the distribution.