Question

Suppose that A is the price of an Apple stock and M is the price of a Microsoft stock. Consider the following statement: Apple has a higher price on average, but Microsoft is more stable. What are the random variables in this situation? Using complete, well thought out sentences, explain which, standard deviaton of Microsoft or standard deviation of Apple, is bigger, Explain which, mean of Microsoft or mean of Apple, is bigger. Be sure to Explain why you think this way.

Answer 1

The random variables are the stock prices of Apple (A) and Microsoft (M). Apple's stock, having a higher average price, has a larger mean, while Microsoft's stock, being more stable, has a smaller standard deviation.

Step-by-step explanation:

In the given scenario, the random variables are the prices of Apple (A) and Microsoft (M) stocks. When it is stated that 'Apple has a higher price on average', it suggests that the expected value or mean of Apple is bigger than that of Microsoft. Similarly, the term 'Microsoft is more stable' implies that the standard deviation of Microsoft stock prices is lower than that of Apple's, indicating less variability in Microsoft's stock prices.

Standard deviation is a measure of how spread out numbers are. If Microsoft stock prices are described as more stable, their standard deviation must be smaller, suggesting the prices do not fluctuate as wildly as those of Apple. Conversely, if Apple's stock prices have a higher mean, this would indicate that, on average, Apple's stock is priced higher than Microsoft's.

The importance of understanding these concepts is not limited to stock market analysis, but is a fundamental aspect of statistics that provides insights into the behavior of different types of data.

Answer 2

The random variables in this situation are the stock prices A and M.

The mean of Apple's stock prices is greater than the mean of Microsoft's stock prices.

The standard deviation of the price of Microsoft shares is smaller than that of Apple's share prices.

Step-by-step explanation:

The random variables in this situation are the stock prices A and M.

According to the text, it is stated that the values of Apple shares are usually higher than those of Microsoft shares. This implies that, since they are random variables, the mean of Apple's stock prices is greater than the mean of Microsoft's stock prices.

In stock prices, the standard deviation is a measure of the risk or stability of a share price. It is a measure of the price variation around its average value. The more stable the value of an action, the smaller the value of the standard deviation.

Then, according to the text, we can affirm that, since Microsoft's prices are more stable, the standard deviation of the price of Microsoft shares must be less than that of Apple's share prices.