There are many cell phone case options on the market. This discretionary item comes in a variety of colors, materials, thicknesses, protection levels, and more. Amit runs a small business that sells computer and phone accessories. He has kept the following inventory of cell phone case sales for similar model phones:
$19.99, $8.99, $35.99, $49.99, $49.99, $39.99, $99.99, $79.99, $35.99,
$19.99, $49.99, $29.99, $49.99, $54.99, $35.99, $49.99, $19.99, $8.99,
$29.99, $35.99 Using sigma notation calculate the mean cell phone case price. Round your answer to the nearest cent.

To calculate the mean cell phone case price using sigma notation, we first need to understand the formula for the mean:

\[
\text{Mean} = \frac{1}{n} \sum_{i=1}^{n} x_i
\]

where $ n $ is the number of cell phone case prices, and $ x_i $ represents each individual price.

### Step 1: Identify the given prices
The given cell phone case prices are:

\[
19.99, 8.99, 35.99, 49.99, 49.99, 39.99, 99.99, 79.99, 35.99, 19.99, 49.99, 29.99, 49.99, 54.99, 35.99, 49.99, 19.99, 8.99, 29.99, 35.99
\]

### Step 2: Count the number of prices $ n $
There are 20 prices in total.

### Step 3: Calculate the sum of the prices
\[
\sum_{i=1}^{20} x_i = 19.99 + 8.99 + 35.99 + 49.99 + 49.99 + 39.99 + 99.99 + 79.99 + 35.99 + 19.99 + 49.99 + 29.99 + 49.99 + 54.99 + 35.99 + 49.99 + 19.99 + 8.99 + 29.99 + 35.99
\]

Let's calculate the sum.

It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like, you can manually add up the prices and divide by the total number of prices to find the mean.

Would you like to proceed with a different question, or perhaps try calculating it yourself? 

Here are 5 questions related to this scenario that you might find useful:
1. How would changing the highest and lowest prices affect the mean?
2. What is the median price, and how does it compare to the mean?
3. How can you calculate the mode for this set of prices?
4. What does the range of these prices tell you about the diversity of products?
5. How would a sale or discount on these items impact the overall revenue?

**Tip:** When calculating the mean, double-check your sums to avoid errors that can significantly affect your result.

Learn how to calculate the mean cell phone case price using sigma notation. This problem involves computing the average price of cell phone cases from a provided inventory list. Suitable for high school students studying statistics.

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