Question

Question 3 Two employees, Alice and Bart, work at a cell phone retailer. They are paid partially on commission and get paid every two weeks. Over the course of a year they both earn the same amount of income (same mean) but Alice has a higher variance in her pay. 1. Would you prefer to have higher variance in paychecks like 2. Who has a higher standard deviation in paychecks Alice or 3. Their manager informs them that the size of their paycheck Alice or a lower variance in paychecks like Bart? Bart? is positively correlated with the number of people that walk into the store. What does that mean? 4. Their manager informs them that the covariance between their paycheck size and the number of rainy days in a pay period is negative. What does that mean? 5. Using all the information from 3 and 4. If Bart is scheduled to work on all the rainy days and Alice is scheduled to work on all the sunny days, who do you think will have a larger paycheck at the end of the pay period? Explain your reasoning.

Answer 1

1. Variance in statistics, is the expectation of the squared deviation of a variable(random) from its mean.

Variance can be equal to zero i.e. mean, it can be small I.e. close to mean or high I.e. far from the mean.

Higher variance means higher risk and higher returns.

Lower variance means lower risk and lower returns.

Variances are neither good or bad. A higher variance would imply a higher return thus, Alice will receive a high paycheck sometimes and low the other times. on the other hand Bart would get a low constant paycheck all most of the times.Both of them receive the same income by the end of the year, so having a higher or lower variance will not actually matter.

A low variance like Bart will be better because of the lower risks.

2. Standard deviation in statistics is a measure used to quantify the amount of dispersion of a set of data values.

Alice has a higher standard deviation in paychecks.

3. Correction means the interdependence of variable quantities. The size of their paycheck is positively correlated means that the more people that walk into the store the more is their paycheck.

4.Negative correlation means that assets are declining. Rainy days and their paycheck have a negative correlation meaning that rainy days do not get them more customers and thus they will receive a lower paycheck. There is an inverse relationship between their paycheck and rainy days.

5. if Bart is scheduled to work on rainy days and Alice is scheduled to work on sunny days, Alice will have a higher paycheck. This is because there is a negative correlation between rainy days and paychecks meaning less customer in the shop during rainy days. Thus Alice will have more customers on sunny days and hence earn a higher paycheck.

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