Question

in a neighborhood donut shop, one type of donut has 580 calories, four types of donuts have 370 calories, seven types of donuts have 600 calories, two types of donuts have 390 calories, and five types of donuts have 360 calories.
find the range.
$\boldsymbol{square}$ calories
find the standard deviation. round your answer to the nearest tenth, if necessary.
$\boldsymbol{square}$ calories
question help: $\boldsymbol{otimes}$ video 1 $\boldsymbol{otimes}$ video 2
submit question

Explanation:

Step1: Identify min and max values

Max calories = 600, Min calories = 360

Step2: Calculate the range

Range = Max - Min = $600 - 360 = 240$

Step3: Calculate total number of donuts

Total = $1 + 4 + 7 + 2 + 5 = 19$

Step4: Calculate the mean

Mean $\bar{x} = \frac{(1\times580)+(4\times370)+(7\times600)+(2\times390)+(5\times360)}{19}$
$\bar{x} = \frac{580 + 1480 + 4200 + 780 + 1800}{19} = \frac{8840}{19} \approx 465.263$

Step5: Calculate sum of squared deviations

Sum = $1\times(580-465.263)^2 + 4\times(370-465.263)^2 + 7\times(600-465.263)^2 + 2\times(390-465.263)^2 + 5\times(360-465.263)^2$
Sum = $1\times(114.737)^2 + 4\times(-95.263)^2 + 7\times(134.737)^2 + 2\times(-75.263)^2 + 5\times(-105.263)^2$
Sum $\approx 13164.5 + 4\times9075.0 + 7\times18154.0 + 2\times5664.5 + 5\times11080.3$
Sum $\approx 13164.5 + 36300.0 + 127078.0 + 11329.0 + 55401.5 = 243273$

Step6: Calculate variance

Variance $s^2 = \frac{243273}{19-1} = \frac{243273}{18} \approx 13515.17$

Step7: Calculate standard deviation

Standard deviation $s = \sqrt{13515.17} \approx 116.255 \approx 116.3$

Answer:

Range: 240 calories
Standard deviation: 116.3 calories