Question

During a 5-week period in 2007, the stock of an insurance company and the stock of a small tech company showed the following weekly percentage changes.

Company Weekly Price Change (%)
Insurance Stock 0.7 -1.7 1.7 -0.3 1.4
Tech Stock 4.8 -3.5 0.7 1.6 -3.4


Find the variance of the weekly price changes of each. (Round your answers to four decimal places.)
insurance stock:
tech stock:

Answer 1

The variance of the weekly price changes for the insurance stock is 4.984, while for the tech stock it is 11.504.

Step-by-step explanation:

To find the variance of the weekly price changes for each stock, we first need to calculate the mean of the weekly price changes for each stock, and then subtract each weekly price change from the mean and square the result. Finally, we average these squared differences to find the variance.

For the insurance stock:

1. Find the mean: (0.7 - 1.7 + 1.7 - 0.3 + 1.4) / 5 = 0.36
2. Subtract the mean from each weekly price change and square the result: (0.7 - 0.36)^2 + (-1.7 - 0.36)^2 + (1.7 - 0.36)^2 + (-0.3 - 0.36)^2 + (1.4 - 0.36)^2 = 24.92
3. Average the squared differences: 24.92 / 5 = 4.984

Therefore, the variance of the weekly price changes for the insurance stock is 4.984 (rounded to four decimal places).

For the tech stock:

1. Find the mean: (4.8 - 3.5 + 0.7 + 1.6 - 3.4) / 5 = 0.64
2. Subtract the mean from each weekly price change and square the result: (4.8 - 0.64)^2 + (-3.5 - 0.64)^2 + (0.7 - 0.64)^2 + (1.6 - 0.64)^2 + (-3.4 - 0.64)^2 = 57.52
3. Average the squared differences: 57.52 / 5 = 11.504

Therefore, the variance of the weekly price changes for the tech stock is 11.504 (rounded to four decimal places).