Problem 75 - Basic Statistics for Business and Economics with Student

Question

There are many financial websites that provide information on stocks by industry. For example, go to http://finance.yahoo.com and select Stock Research under Analyst Research select Sector/Industry Analysis. There are many choices available here such as Healthcare. Another list of choices is now available; select one such as Drug Manufacturers-Major. A list of companies in that industry will appear. Select one of the variables available, such as the price to earnings ratio, listed as \(\mathbf{P} / \mathbf{E} .\) This variable is the ratio of the selling price of a share of the company's common stock to the earnings per share of common stock. Download this information into Excel and find the mean, median, and standard deviation. Go back to Sector/Industry Analysis and choose another sector and industry. You might want to select Utilities and then Gas Utilities. A list of companies will appear. Select the same variable as before. Download the information to Excel and find the mean, median, and standard deviation for this industry. Compare the information on the two sectors. Write a brief report summarizing your findings. Are the means different? Is there more variability in one industry than another?

Step-by-Step Solution

Answer

Calculate the mean, median, and standard deviation for P/E ratios in two industries; compare differences and report.

Step 1: Access Financial Data

Visit the website http://finance.yahoo.com. Navigate to Stock Research and select Sector/Industry Analysis. Choose a sector like Healthcare, and then select a specific industry such as Drug Manufacturers-Major. This will give you a list of companies in that industry.

Step 2: Select and Download the Variable Data

From the list of companies in the chosen industry, select the variable \( P/E \) ratio. Download this data to Excel. Repeat these steps for another sector, like Utilities, and an industry under it, such as Gas Utilities.

Step 3: Calculate the Mean

In Excel, use the \( \text{AVERAGE}() \) function to calculate the mean of the \( P/E \) ratios for each industry you downloaded data for (e.g., Drug Manufacturers-Major and Gas Utilities).

Step 4: Calculate the Median

Use the \( \text{MEDIAN}() \) function in Excel to find the median \( P/E \) ratio for each industry.

Step 5: Calculate the Standard Deviation

Utilize the \( \text{STDEV.S}() \) function in Excel to determine the standard deviation of the \( P/E \) ratios for both industries.

Step 6: Compare the Mean and Variability

Compare the mean \( P/E \) ratios between the two industries to see which one has a higher average. Also, compare the standard deviation values to evaluate which industry has more variability in the \( P/E \) ratios.

Step 7: Write a Summary Report

Write a brief report summarizing your findings. Indicate whether the means of the \( P/E \) ratios are different between the two industries and discuss if one industry shows more variability in \( P/E \) ratios based on the standard deviations.

Key Concepts

Mean Calculation

Calculating the mean is a fundamental aspect of statistical analysis. It's a great way to get an overall idea of the data set. Simply put, the mean is the average value of a set of numbers.
In financial terms, it helps us understand the average performance of a particular metric, such as the price to earnings (P/E) ratio.
Let's break down how to calculate it:

• Add up all the numbers in your data set.
• Count how many numbers are in the set.
• Divide the total sum by the count of numbers.

For instance, if the P/E ratios in your industry are 10, 15, and 20, you would add these up to get 45.
Then, since there are 3 numbers, you divide 45 by 3 to get a mean P/E ratio of 15.
This simple calculation provides a quick glimpse at the central tendency of the ratios in your selected industry.
When comparing different industries, say Drug Manufacturers-Major and Gas Utilities, the mean P/E ratio can reveal much about the average investor expectations in these sectors.

Median Calculation

The median offers another way to measure the center of a data set and can be particularly useful when data points are skewed or when there are outliers.
Unlike the mean, the median doesn't get influenced by extremely high or low values. This makes it an important statistic, especially in finance data.
Here's how to find it:

• First, sort your data set in increasing order.
• If there's an odd number of data points, the median is the middle number.
• If there's an even number, it is the average of the two middle numbers.

Consider a sorted set of P/E ratios: 8, 9, 10, 11, and 50. The median is 10, which sits right in the middle.
Notice how the high value of 50 doesn’t affect the median like it would the mean.
This measure is particularly insightful when comparing sectors with different data distributions.
It gives a clearer picture in cases where one industry might have outliers or an uneven spread of P/E ratios, such as in rapidly growing tech companies versus more stable utilities.

Standard Deviation

Standard deviation is a tool that provides insights into the amount of variation or dispersion in a set of data points.
In the context of P/E ratios, it shows how much these ratios fluctuate from the average.
Here’s the basic process to calculate it:

• Find the mean of your data set.
• Subtract the mean from each data point and square the result.
• Find the mean of these squared differences.
• Take the square root of this mean.

For instance, consider P/E ratios of 10, 15, and 20 again. With a mean of 15:

• The deviations are -5, 0, and 5, respectively.
• Squaring these gives 25, 0, and 25.
• The average of 25, 0, and 25 is approximately 16.67.
• Taking the square root gives a standard deviation of about 4.08.

Standard deviation is crucial for understanding the risk associated with investing in a particular sector.
The higher the standard deviation, the more variation there is in the data set, which corresponds to greater risk.
When you compare industries, those with higher standard deviations in their P/E ratios, like tech sectors, could imply more volatile earnings compared to more stable industries, such as utilities.