Let's find some statistical measures for the given dataset, which consists of the ages of teachers:

Ages: 18, 21, 20, 17, 23, 31, 35, 28

1. Mean (Average) Age

The mean is the sum of the ages divided by the number of teachers.

$\text{Mean} = \frac{18 + 21 + 20 + 17 + 23 + 31 + 35 + 28}{8} = \frac{193}{8} = 24.125$

2. Median Age

To find the median, arrange the ages in ascending order:

17, 18, 20, 21, 23, 28, 31, 35

The median is the middle value. Since there are 8 numbers, the median will be the average of the 4th and 5th numbers:

$\text{Median} = \frac{21 + 23}{2} = \frac{44}{2} = 22$

3. Mode

The mode is the most frequent number in the dataset. Since no number repeats, there is no mode.

4. Range

The range is the difference between the highest and lowest ages.

$\text{Range} = 35 - 17 = 18$

5. Variance and Standard Deviation

To compute the variance, find the difference between each age and the mean, square it, and then average these squared differences.

$\text{Variance} = \frac{(18-24.125)^2 + (21-24.125)^2 + \ldots + (28-24.125)^2}{8}$

Let's calculate this step by step.

5. Variance and Standard Deviation (Continued)

• Variance: $37.11$ (approximately)
• Standard Deviation: $6.09$ (approximately)

Summary of Statistical Measures:

• Mean: 24.125
• Median: 22
• Mode: None
• Range: 18
• Variance: 37.11
• Standard Deviation: 6.09

Would you like to go into more details on any of these measures, or do you have any questions?

Here are 5 follow-up questions for you:

1. How is the variance useful in understanding this dataset?
2. What is the significance of the standard deviation?
3. How would the median change if one of the values was an outlier?
4. Can we interpret the range alone to understand data spread effectively?
5. How can mode be relevant in a dataset like this?

Tip: When comparing data sets, standard deviation helps you understand how spread out the values are. A smaller standard deviation indicates that the data points tend to be closer to the mean.