The net incomes of a sample of importers were organized into the following table:
Net Income (in $ millions) Number of Importers
2 - 41
5 - 74
8 - 1010
11 - 133
14 - 162
What is the mean net income?
Click on the arrows to vote for the correct answer
A. B. C. D. E.D
(3*1)+(6*4)+(9*10)+(12*3)+(15*2) = 183. Mean is 183/20 = 9.15
To find the mean net income, we need to calculate the average of the net incomes provided in the table.
First, we can calculate the midpoint for each interval by taking the average of the lower and upper bounds. Then, we multiply each midpoint by its corresponding frequency (number of importers) to get the total income for each interval. Finally, we sum up all the total incomes and divide by the total number of importers to obtain the mean net income.
Let's calculate it step by step:
2 | 4 | 3 | 41 | 3 * 41 = 123 5 | 7 | 6 | 74 | 6 * 74 = 444 8 | 10 | 9 | 1010 | 9 * 1010 = 9090 11 | 13 | 12 | 133 | 12 * 133 = 1596 14 | 16 | 15 | 162 | 15 * 162 = 2430
Now, we sum up all the total incomes: Total Income = 123 + 444 + 9090 + 1596 + 2430 = 13683
Next, we sum up all the frequencies to find the total number of importers: Total Importers = 41 + 74 + 1010 + 133 + 162 = 1420
Finally, we can calculate the mean net income by dividing the total income by the total number of importers: Mean Net Income = Total Income / Total Importers = 13683 / 1420 ≈ $9.6338 million
Rounded to the nearest million, the mean net income is approximately $9.00 million.
Therefore, the correct answer is E. $9.00 million.