Let's start by calculating the mean, median, and mode(s) for the given silver prices:

Silver Prices for 10 Business Days:

19.5, 19.2, 19.3, 19.2, 19, 18.7, 18.7, 18.7, 19.1, 18.8

1. Sample Mean:

The sample mean is calculated by summing all the values and dividing by the number of observations (10 in this case).

$\text{Mean} = \frac{19.5 + 19.2 + 19.3 + 19.2 + 19 + 18.7 + 18.7 + 18.7 + 19.1 + 18.8}{10}$

Let me compute that.

2. Sample Median:

The median is the middle value in the sorted list. If there are an even number of observations, the median is the average of the two middle values. Sorting the prices gives us:

$18.7, 18.7, 18.7, 18.8, 19, 19.1, 19.2, 19.2, 19.3, 19.5$

Since there are 10 values, the median is the average of the 5th and 6th values.

$\text{Median} = \frac{19 + 19.1}{2}$

Let me compute that.

3. Mode(s):

The mode is the value(s) that appears most frequently in the data. Looking at the sorted list:

$18.7 \text{ appears 3 times}, 19.2 \text{ appears 2 times}.$

So, the mode is 18.7.

Let me now calculate the mean and median.Here are the results:

1. Sample Mean: $19.02$
2. Sample Median: $19.05$
3. Mode(s): $18.7$

Interpretation:

Over the 10-business-day period sampled, the price of silver averaged $19.02 per ounce. It was above $19.05 as many times as it was below that price, and stood at $18.7 per ounce more often than at any other price.

Would you like further details or explanations? Here are some related questions to deepen your understanding:

1. How would the mean and median change if the highest value (19.5) was higher or lower?
2. Why might the mode be useful in understanding typical price levels in this dataset?
3. How does the presence of multiple modes affect the interpretation of the data?
4. Can a dataset have no mode? What would that imply in terms of silver prices?
5. How would outliers (extremely high or low prices) affect the mean and median?

Tip: The median is often preferred over the mean for summarizing skewed data or when there are outliers.