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2-81.

The Food and Drug Administration requires that restaurants with more than $20$ locations post the calories of their food items online and on their menus. Salvatore Giacobassi, the owner of Pollo Genio, must publish the calories in their famous Ala di Pollo Extravaganza, a dish which includes several batter‑fried chicken wings.

An inspector chooses a random sample of $30$ wings and measures the calorie content of each. The data is sorted and shown at right.

 $121.2$ $146.3$ $169.5$ $125.7$ $147.4$ $170.7$ $126.2$ $147.6$ $170.8$ $126.9$ $152.8$ $173.2$ $128.2$ $155.2$ $173.5$ $135.7$ $156.7$ $180.1$ $139.7$ $157.0$ $181.4$ $141.8$ $157.0$ $184.5$ $143.0$ $160.5$ $196.1$ $143.8$ $163.3$ $261.0$ Checksum $4736.8$
1. Construct a histogram of the calorie data. Begin with your lowest bin at $120$ calories and use a bin width of $20$ calories.

2. Why did the inspector test $30$ wings when it would have been much easier and less expensive to test just one?

There is a lot of variation in the calorie content of a batter fried chicken wings. Chickens are not all the same size and the amount of batter stuck to the wings can also vary.

3. The FDA calculated the following statistics from the data: (calories)

Mean $\approx157.9$   Standard Deviation $\approx27.5$   Median $\approx156.0$   IQR $=29.0$

Which set of measures best describes the calories in a typical Pollo Genio batter‑fried chicken wing?  Justify your answer.

If the data is symmetric with no outliers, the mean and standard deviation can be used to describe the center and spread.