The stock prices of a company over five consecutive days are $150, $155, $148, $152, and

$149.

- What is the average stock price over this period?

- Calculate the sample variance, variance, and standard deviation of the stock prices.

Let's solve the two parts of your question:

### 1. **Average Stock Price:**

The average (mean) stock price over the five days can be calculated using the formula for the mean:

\[
\text{Mean} = \frac{\sum \text{Stock Prices}}{\text{Number of Days}}
\]

Given the stock prices are $150, $155, $148, $152, and $149:

\[
\text{Mean} = \frac{150 + 155 + 148 + 152 + 149}{5}
\]

Let's compute this.

### 2. **Variance, Sample Variance, and Standard Deviation:**

- **Sample Variance** ($s^2$): 

For the sample variance, we use:

\[
s^2 = \frac{\sum (x_i - \bar{x})^2}{n - 1}
\]

where $x_i$ are the individual stock prices, $\bar{x}$ is the mean stock price, and $n$ is the number of stock prices (5 in this case).

- **Population Variance** ($\sigma^2$): 

If we consider this a population, the variance formula is:

\[
\sigma^2 = \frac{\sum (x_i - \bar{x})^2}{n}
\]

- **Standard Deviation** (both sample and population):

The standard deviation is the square root of the variance.

Let's calculate these values step-by-step.### Results:

1. **Average Stock Price:**
   \[
   \text{Mean} = 150.8
   \]

2. **Sample Variance** ($s^2$):
   \[
   s^2 = 7.7
   \]

3. **Population Variance** ($\sigma^2$):
   \[
   \sigma^2 = 6.16
   \]

4. **Sample Standard Deviation** ($s$):
   \[
   s \approx 2.77
   \]

5. **Population Standard Deviation** ($\sigma$):
   \[
   \sigma \approx 2.48
   \]

These values summarize the spread and variability of the stock prices over the given period.

Would you like to dive deeper into any of these calculations or explore related topics?

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### 5 Related Questions:
1. How do you interpret variance and standard deviation in a stock market context?
2. What is the difference between sample variance and population variance?
3. How does one use standard deviation to measure stock volatility?
4. How do changes in stock prices affect the standard deviation?
5. How can one calculate the moving average for stock prices?

### Tip:
Understanding the difference between sample and population statistics is crucial for analyzing real-world data accurately!

Learn how to calculate the average stock price, sample variance, population variance, sample standard deviation, and population standard deviation for a series of stock prices. Detailed step-by-step solution and formulas provided.

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