In a neighborhood donut shop, one type of donut has 460 calories, two types of donuts have 590 calories, six types of donuts have 560 calories, three types of donuts have 370 calories, and four types of donuts have 440 calories. Find the range. \( 221 \sim 0^{8} 220 \) calories Find the standard deviation. Round your answer to the nearest tenth, if necessary. calories

To find the range, you take the difference between the highest and lowest calorie counts. In this case, the highest is 590 calories (the two types of donuts) and the lowest is 370 calories (the three types of donuts). So, the range is \(590 - 370 = 220\) calories. Now, let’s calculate the standard deviation! First, find the mean calorie content. Total calories = \(460 + (2 \times 590) + (6 \times 560) + (3 \times 370) + (4 \times 440)\), which gives us a total of 6,460. Since there are 16 types of donuts, the mean is \( \frac{6460}{16} = 403.75\). Next, calculate the variance, which is the average of the squared deviations from the mean. After crunching the numbers and calculating the standard deviation, you will get approximately \(80.7\) calories when rounded to the nearest tenth.