Question

Phaedra researched the cost of a gallon of milk at eight grocery stores. She recorded her data below. Find the mean cost of a gallon of milk and the mean absolute deviation of the data set: $3.50, $3.50, $2.50, $2.50, $5.00, $2.50, $4.00, $4.50

(a) Mean cost: $3.38, Mean absolute deviation: $0.50
(b) Mean cost: $3.50, Mean absolute deviation: $0.83
(c) Mean cost: $3.69, Mean absolute deviation: $0.75
(d) Mean cost: $4.00, Mean absolute deviation: $0.60

Answer 1

The mean cost of a gallon of milk from the provided data is $3.50, and the mean absolute deviation is $0.75. The correct answer choice is (b).

Step-by-step explanation:

To find the mean cost of a gallon of milk from the data provided, we sum all the costs and divide by the number of observations (eight grocery stores). The total cost of all the gallons is $3.50 + $3.50 + $2.50 + $2.50 + $5.00 + $2.50 + $4.00 + $4.50, which equals $28.00. Dividing $28.00 by 8 gives us a mean cost of $3.50.

Next, we calculate the mean absolute deviation (MAD). To do this, we take the absolute value of the difference between each data point and the mean, then find the average of those differences. The differences are $0.00, $0.00, $1.00, $1.00, $1.50, $1.00, $0.50, and $1.00. Adding these up gives us $6.00. Dividing by the number of data points, 8, we get the MAD of $0.75.

Therefore, the correct answer is (b) Mean cost: $3.50, Mean absolute deviation: $0.75.