Question

analyzing tax data
the table presents detailed tax data for 10 individuals, including their respective incomes, taxes paid, deductions, and tax refunds.
table with columns: tax id, income ($), tax paid ($), deductions ($), tax refund ($) and rows for id001 to id010 with respective values
if the income of id003 (originally $114,950) was entered incorrectly and should be $100,000, what would be the new mean income?
enter your answer in the box.

Explanation:

Step1: Calculate the sum of original incomes

First, we list the original incomes: 78340, 51270, 114950, 88560, 47380, 104870, 67490, 83240, 91760, 57210.
Sum them up: \(78340 + 51270 + 114950 + 88560 + 47380 + 104870 + 67490 + 83240 + 91760 + 57210\)
Let's calculate step by step:
\(78340+51270 = 129610\)
\(129610+114950 = 244560\)
\(244560+88560 = 333120\)
\(333120+47380 = 380500\)
\(380500+104870 = 485370\)
\(485370+67490 = 552860\)
\(552860+83240 = 636100\)
\(636100+91760 = 727860\)
\(727860+57210 = 785070\)

Step2: Adjust the sum for ID003

The original income for ID003 is 114950, and the correct income is 100000. So we need to subtract the original amount and add the correct amount.
Adjustment: \(785070 - 114950 + 100000\)
Calculate: \(785070 - 114950 = 670120\); \(670120 + 100000 = 770120\)

Step3: Calculate the new mean

There are 10 individuals, so the mean is the adjusted sum divided by 10.
Mean = \(\frac{770120}{10} = 77012\)

Answer:

77012