Let's go through each of the questions in detail:

5. Finding the Mean, Median, and Mode for the Variable Age

Mean

The mean (average) is calculated by summing all the ages and dividing by the number of ages.

Median

To find the median, we need to order the ages from smallest to largest and then find the middle value. If there is an odd number of observations, the median is the middle value. If there is an even number of observations, the median is the average of the two middle values.

Mode

The mode is the age that appears most frequently in the dataset.

6. Five-Number Summary for the Students' Ages

The five-number summary includes:

1. Minimum: The smallest age in the dataset.
2. First Quartile (Q1): The median of the first half of the dataset.
3. Median (Q2): The middle value of the dataset.
4. Third Quartile (Q3): The median of the second half of the dataset.
5. Maximum: The largest age in the dataset.

7. Lower and Upper Fences for the Students' Ages

The fences help identify potential outliers:

• Lower Fence: $Q1 - 1.5 \times \text{IQR}$
• Upper Fence: $Q3 + 1.5 \times \text{IQR}$

where IQR (Interquartile Range) is calculated as $Q3 - Q1$.

Let's compute these values step by step.

Step 1: Organize and Count the Data

I'll count and organize the data first to make the calculations clearer.

Step 2: Calculations

Let's proceed with these calculations now.Here are the calculated values:

5. Mean, Median, and Mode

• Mean (Average): 29.17 (rounded to two decimal places)
• Median: 26.0
• Mode: 23 (the age that appears most frequently)

6. Five-Number Summary

• Minimum: 20
• First Quartile (Q1): 24.0
• Median (Q2): 26.0
• Third Quartile (Q3): 32.0
• Maximum: 59

7. Lower and Upper Fences

• Lower Fence: 12.0
• Upper Fence: 44.0

These fences indicate that any ages below 12 or above 44 could be considered potential outliers in this dataset.

Would you like more details on any part of the calculation or have further questions?

Here are some follow-up questions to expand on this:

1. How can we interpret the five-number summary in terms of age distribution?
2. What is the significance of identifying outliers in this dataset?
3. How does the presence of outliers affect the mean and median?
4. Can we use other measures like standard deviation for a similar analysis?
5. How would the calculations change if we removed the outliers?

Tip: The median is often a better measure of central tendency than the mean in skewed distributions, as it is less affected by extreme values.