Question 1

In a neighborhood donut shop, one type of donut has 420 calories, three types of donuts have 580 calories, four types of donuts have 390 calories, six types of donuts have 600 calories, and three types of donuts have 450 calories.

Find the range.
calories

Find the standard deviation. Round your answer to the nearest tenth, if necessary.
calories

Question Help: $\square$ Video 1 Video 2
Submit Question

Step 1 ：First, we need to identify the highest and lowest calorie counts among the donuts. The highest calorie count is 600 calories and the lowest is 390 calories.

Step 2 ：Next, we calculate the range by subtracting the lowest calorie count from the highest. This gives us a range of \(600 - 390 = 210\) calories.

Step 3 ：To calculate the standard deviation, we first need to find the mean (average) of the calorie counts. We add up all the calorie counts and divide by the total number of donuts.

Step 4 ：Then, we subtract the mean from each individual calorie count and square the result. We add up all these squared differences and divide by the total number of donuts to find the variance.

Step 5 ：Finally, we take the square root of the variance to find the standard deviation. The standard deviation of the calories is approximately 93.5 calories.

Step 6 ：So, the range of the calories is \(\boxed{210}\) and the standard deviation of the calories is \(\boxed{93.5}\).