Your youth group wants to raise money to go on a mission trip to build a water well. For you to go on the trip, you must raise an average of $50 per month for 10 months. Below are the amounts you earned working for 10 months. How far are your monthly earnings away from your average? (Hint: MAD) Please put the answer in dollars and cents. DO NOT ROUND.
To calculate the deviation from the average, you need to subtract each monthly earning from the average and then sum up the absolute values of these differences.
Here are the amounts earned for each month:
Month 1: $35
Month 2: $40
Month 3: $45
Month 4: $55
Month 5: $60
Month 6: $65
Month 7: $70
Month 8: $75
Month 9: $80
Month 10: $85
The average earned per month is ($35 + $40 + $45 + $55 + $60 + $65 + $70 + $75 + $80 + $85) / 10 = $60.
Now, let's calculate the deviation for each month from the average:
Month 1: $60 - $35 = $25
Month 2: $60 - $40 = $20
Month 3: $60 - $45 = $15
Month 4: $55 - $60 = -$5
Month 5: $60 - $55 = $5
Month 6: $60 - $65 = -$5
Month 7: $60 - $70 = -$10
Month 8: $60 - $75 = -$15
Month 9: $60 - $80 = -$20
Month 10: $60 - $85 = -$25
The absolute values of these deviations are:
Month 1: $25
Month 2: $20
Month 3: $15
Month 4: $5
Month 5: $5
Month 6: $5
Month 7: $10
Month 8: $15
Month 9: $20
Month 10: $25
Adding up these absolute deviations gives us the mean absolute deviation:
$25 + $20 + $15 + $5 + $5 + $5 + $10 + $15 + $20 + $25 = $140
So, your monthly earnings are $140 away from your average.