Please help thank you!! Standard Deviation

Question

In a neighborhood donut shop, one type of donut has 410 calories, six types of donuts have 520 calories, five types of donuts have 340 calories, three types of donuts have 500 calories, and six types of donuts have 570 calories.

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

Answer 1

To find the standard deviation of the calorie distribution, we need to first calculate the mean or the average calorie content. We can do this by finding the weighted average of the calorie content of each type of donut, where the weights are the number of each type of donut.

The total number of types of donuts is 21, so we can calculate the mean calorie content as:

mean = (1410 + 6520 + 5340 + 3500 + 6*570) / 21 = 470 calories

Next, we can calculate the variance of the distribution by finding the weighted sum of squared deviations from the mean:

variance = [1*(410-470)^2 + 6*(520-470)^2 + 5*(340-470)^2 + 3*(500-470)^2 + 6*(570-470)^2] / 21 = 15560 / 21 = 741.9

Finally, we can take the square root of the variance to obtain the standard deviation:

standard deviation = sqrt(variance) ≈ 27.2 calories

Therefore, the standard deviation of the calorie distribution is approximately 27.2 calories, rounded to the nearest tenth.