1. An economist is analyzing the monthly incomes (in thousands of dollars) of a small sample of households in a neighborhood to understand income distribution. The incomes of eight households are recorded as follows:
Monthly Income (in $1000s): 4.2, 5.8, 6.3, 5.7, 6.5, 7.5
(a) [1.5 marks] Calculate the mean, median, and mode of the monthly incomes by hand.
(b) [2 marks] Calculate the variance and standard deviation of the incomes by hand. Show your calculations.
(c) [1.5 marks] Suppose a tax adjustment doubles every household's income. What would the new standard deviation be? Explain how you determined your answer.