Question

What's the answer to this problem?

Answer 1

Answers:

• MAD of the expensive dishes = 3.6
• MAD of the cheapest dishes = 1.76
• The MAD of 1.76 (least expensive) is much less than the MAD of 3.6 (most expensive)
• So the data for the five least expensive dishes is closer together compared to the most expensive dishes.

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Explanation:

For now, focus on the most expensive dishes only.

Add up the values and divide by 5 to get the mean.

(28+30+28+39+25)/5 = 150/5 = 30

The mean is 30

Subtract this mean from each of the prices. Use absolute value to ensure the difference is never negative.

• |28-30| = 2
• |30-30| = 0
• |28-30| = 2
• |39-30| = 9
• |25-30| = 5

This represents the distance each value is from the mean. For example, the value 25 is 5 units from the mean.

Then we average the set {2,0,2,9,5} to get the mean of (2+0+2+9+5)/5 = 18/5 = 3.6

The mean absolute deviation (MAD) for the most expensive dishes is 3.6

This is the average distance each value is from the mean. It's one measure to see how spread out a group of numbers is. The higher the MAD, the more spread out the values, and vice versa.

If you repeated those steps for the least expensive dishes, then you should get a MAD of 1.76

We see that the MAD of the cheaper dishes is much smaller than the expensive ones. This tells us the cheaper dishes are more clumped together, and closer to the mean. In other words, the cheaper dishes are more consistent in price. The expensive dishes are more spread out.