*Earnings per* 

*share*. 

The earnings per share​ (in dollars) for 12 companies selected at random from the list of Fortune 500 companies​ are:

0.530.53

0.550.55

6.076.07

6.656.65

1.851.85

8.428.42

6.796.79

6.546.54

1.911.91

1.591.59

8.488.48

8.498.49

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Part 1

**a.** Find the mean of the earnings per share. 

​$4.824.82

​(Type an integer or a decimal. Round to two decimal​ places.)

Part 2

**b.** Find the standard deviation of the earnings per share. 

​$enter your response here

​(Type an integer or a decimal. Round to two decimal​ places.)




To find the standard deviation of the earnings per share (EPS), we follow these steps:

### Step 1: Calculate the Mean
We've already calculated the mean of the EPS, which is $ \mu = 4.82 $.

### Step 2: Calculate Each Deviation from the Mean
Subtract the mean from each EPS value to find the deviation of each value from the mean.

\[
\text{Deviations} = 
\begin{aligned}
&0.53 - 4.82 = -4.29 \\
&0.55 - 4.82 = -4.27 \\
&6.07 - 4.82 = 1.25 \\
&6.65 - 4.82 = 1.83 \\
&1.85 - 4.82 = -2.97 \\
&8.42 - 4.82 = 3.60 \\
&6.79 - 4.82 = 1.97 \\
&6.54 - 4.82 = 1.72 \\
&1.91 - 4.82 = -2.91 \\
&1.59 - 4.82 = -3.23 \\
&8.48 - 4.82 = 3.66 \\
&8.49 - 4.82 = 3.67 \\
\end{aligned}
\]

### Step 3: Square Each Deviation
Next, square each of the deviations calculated above:

\[
\text{Squared Deviations} =
\begin{aligned}
&(-4.29)^2 = 18.40 \\
&(-4.27)^2 = 18.23 \\
&(1.25)^2 = 1.56 \\
&(1.83)^2 = 3.35 \\
&(-2.97)^2 = 8.82 \\
&(3.60)^2 = 12.96 \\
&(1.97)^2 = 3.88 \\
&(1.72)^2 = 2.96 \\
&(-2.91)^2 = 8.47 \\
&(-3.23)^2 = 10.43 \\
&(3.66)^2 = 13.40 \\
&(3.67)^2 = 13.47 \\
\end{aligned}
\]

### Step 4: Find the Mean of the Squared Deviations
Add all the squared deviations together, then divide by the number of companies (n = 12):

\[
\text{Sum of Squared Deviations} = 18.40 + 18.23 + 1.56 + 3.35 + 8.82 + 12.96 + 3.88 + 2.96 + 8.47 + 10.43 + 13.40 + 13.47 = 116.93
\]

\[
\text{Variance} (\sigma^2) = \frac{116.93}{12} = 9.7442
\]

### Step 5: Take the Square Root of the Variance
Finally, the standard deviation is the square root of the variance:

\[
\text{Standard Deviation} (\sigma) = \sqrt{9.7442} \approx 3.12
\]

### Answer
The standard deviation of the earnings per share is approximately **$3.12**.

Would you like any further explanation on this?

---

Here are some related questions:

1. What does the standard deviation tell us about the data spread?
2. How would the standard deviation change if one EPS value were significantly different?
3. How does the standard deviation compare to the mean in this context?
4. What is the significance of a higher standard deviation in financial data?
5. How can the variance be interpreted alongside the standard deviation?
6. What role does standard deviation play in risk assessment for companies?
7. How does standard deviation differ from mean absolute deviation?
8. How might a portfolio manager use standard deviation in investment decisions?

**Tip:** Standard deviation provides insight into the volatility or variability in a dataset. A higher standard deviation indicates more spread out data points.

Learn how to calculate the mean and standard deviation of earnings per share (EPS) for a set of companies. Understand the significance of these statistical measures in financial analysis. Suitable for undergraduate level students and professionals.

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