Let's first break down the stem-and-leaf plot and extract the data:

Stem-and-Leaf Plot Interpretation:

• 0 | 3 4 → 3, 4
• 1 | 0 4 5 5 6 → 10, 14, 15, 15, 16
• 2 | 1 2 2 3 7 8 → 21, 22, 22, 23, 27, 28
• 3 | 1 7 8 9 → 31, 37, 38, 39
• 4 | 5 9 9 → 45, 49, 49

Data Set:

3, 4, 10, 14, 15, 15, 16, 21, 22, 22, 23, 27, 28, 31, 37, 38, 39, 45, 49, 49

1. Mean:

The mean is the sum of all values divided by the number of values.

To calculate the mean: $\text{Mean} = \frac{\sum \text{data}}{\text{Number of data points}}$ Sum of the data: $3 + 4 + 10 + 14 + 15 + 15 + 16 + 21 + 22 + 22 + 23 + 27 + 28 + 31 + 37 + 38 + 39 + 45 + 49 + 49 = 490$

Number of data points: 20

$\text{Mean} = \frac{490}{20} = 24.5$

2. Median:

The median is the middle value when the data is arranged in order. For an even number of data points, the median is the average of the two middle values.

Arranged data: 3, 4, 10, 14, 15, 15, 16, 21, 22, 22, 23, 27, 28, 31, 37, 38, 39, 45, 49, 49

There are 20 values, so the median will be the average of the 10th and 11th values.

10th value: 22
11th value: 23

$\text{Median} = \frac{22 + 23}{2} = 22.5$

3. Mode:

The mode is the number that appears most frequently.

From the data set, we see that:

• 15 appears twice
• 22 appears twice
• 49 appears twice

So, the modes are 15, 22, and 49.

Summary:

• Mean = 24.5
• Median = 22.5
• Mode(s) = 15, 22, 49

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Using Google Sheets:

1. Enter the Data: Type the data into a column in Google Sheets.
2. Calculate the Mean:
   • In an empty cell, type: =AVERAGE(A1:A20) (assuming your data is in cells A1 to A20).
3. Calculate the Median:
   • In an empty cell, type: =MEDIAN(A1:A20).
4. Calculate the Mode:
   • In an empty cell, type: =MODE(A1:A20) for a single mode or =MODE.MULT(A1:A20) for multiple modes.

Would you like further details or clarification on these steps? Let me know if you need help with Google Sheets.

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Here are some follow-up questions to expand the concepts:

1. How would the mean change if a large outlier was added to the data set?
2. What happens to the median if we rearrange the data set in descending order?
3. Can a data set have no mode? If so, when does this occur?
4. How does the presence of multiple modes affect the interpretation of the data?
5. What is the difference between the mean, median, and mode in terms of their sensitivity to skewed data?

Tip: When dealing with data that may have extreme values, the median can sometimes be a better measure of central tendency than the mean, since it is less affected by outliers.