A scientists income over 3 years was $72,000, $76,000, and $77,000. He won an award the next year, so his income was $1,080,000. By how much does the outlier increase the scientist mean annual income?
Pleas help me and work out the problem
Find the mean with and without the outlier.
So what is that
Which number is much larger than the other three numbers?
To calculate the increase in the scientist's mean annual income caused by the outlier, we need to compare the mean income without the outlier to the mean income with the outlier.
First, let's calculate the mean income without the outlier:
Mean income without outlier = (Sum of incomes - Outlier) / (Number of incomes - 1)
Sum of incomes without outlier = $72,000 + $76,000 + $77,000 = $225,000
Number of incomes without outlier = 3
Mean income without outlier = $225,000 / 3 = $75,000
Next, we calculate the mean income with the outlier:
Mean income with outlier = (Sum of incomes) / (Number of incomes)
Sum of incomes with outlier = $72,000 + $76,000 + $77,000 + $1,080,000 = $1,305,000
Number of incomes with outlier = 4
Mean income with outlier = $1,305,000 / 4 = $326,250
Now, we can calculate the increase in the mean annual income caused by the outlier:
Increase = Mean income with outlier - Mean income without outlier
Increase = $326,250 - $75,000 = $251,250
Therefore, the outlier increases the scientist's mean annual income by $251,250.