Question

MODELING REAL LIFE The table shows the prices of the five most-expensive and least-expensive dishes on a menu. A two-column table. The left column is titled, Five Most-Expensive Dishes. The values in the column are 28 dollars, 30 dollars, 28 dollars, 39 dollars, 25 dollars. The right column is titled, Five Least-Expensive Dishes. The values in the column are 7 dollars, 7 dollars, 10 dollars, 8 dollars, 12 dollars.

Answer 1

The first one is 30. The second is 8.80 to compare your answers are right.

Answer 2

The mean absolute deviation of the five most-expensive dishes is 3.6 and for the five least-expensive dishes, it is 1.76. The MAD demonstrates that the least-expensive dishes have less variation in prices compared to the most-expensive dishes.

To find the mean absolute deviation (MAD) for the two sets of dish prices, we first need to calculate the mean (average) for each set:

For the most-expensive dishes: (28 + 30 + 28 + 39 + 25) / 5 = 150 / 5 = 30.

For the least-expensive dishes: (7 + 7 + 10 + 8 + 12) / 5 = 44 / 5 = 8.8.

Now, we calculate the mean absolute deviation for each set:

For the most-expensive dishes: (|28 - 30| + |30 - 30| + |28 - 30| + |39 - 30| + |25 - 30|) / 5 = (2 + 0 + 2 + 9 + 5) / 5 = 18 / 5 = 3.6.

For the least-expensive dishes: (|7 - 8.8| + |7 - 8.8| + |10 - 8.8| + |8 - 8.8| + |12 - 8.8|) / 5 = (1.8 + 1.8 + 1.2 + 0.8 + 3.2) / 5 = 8.8 / 5 = 1.76.

Comparatively, the MAD of five least-expensive dishes is much less (1.76) than the MAD of five most-expensive dishes (3.6), meaning the least-expensive dishes have smaller variations in their prices and are closer together compared to the most-expensive dishes.