In a neighborhood donut shop, One type of donut has 490 calories, Three types of donuts have 520 calories, Three types of donuts have 360 calories, five types of donuts have 350 calories, and four types of donuts have 390 calories.

Find the standard deviation round answer to the nearest 10th

Can I please have some help

Of course, I'd be happy to help! Calculating the standard deviation involves a bit of math, but don't worry, I'm here to add a little humor to make it more digestible!

To find the standard deviation for the calorie counts of the donuts, follow these steps:

1. List out the calorie counts and their frequencies:
- 490 calories (1 type)
- 520 calories (3 types)
- 360 calories (3 types)
- 350 calories (5 types)
- 390 calories (4 types)

2. Calculate the mean (average) of the calorie counts:
- (490 + (520 x 3) + (360 x 3) + (350 x 5) + (390 x 4)) / (1 + 3 + 3 + 5 + 4)

3. Calculate the squared difference between each calorie count and the mean:
- For example, for 490 calories: (490 - mean)^2
- Repeat this for all the calorie counts.

4. Calculate the sum of all the squared differences.

5. Divide the sum of squared differences by the total number of data points minus one.

6. Finally, take the square root of that number to find the standard deviation.

Remember, it's okay to use a calculator for these calculations, but make sure it doesn't get too calorie-b-rrrrr-ing!

To find the standard deviation, we need to calculate the mean and variance of the given data.

First, let's calculate the mean (average) of the calories of the different types of donuts.

Mean (µ) = (490 + 3(520) + 3(360) + 5(350) + 4(390)) / (1 + 3 + 3 + 5 + 4)
= (490 + 1560 + 1080 + 1750 + 1560) / 16
= 6440 / 16
= 402.5 calories

Next, let's calculate the variance. The variance (σ²) is the average of the squared differences between each observation and the mean.

Variance (σ²) = [(490 - 402.5)² + 3(520 - 402.5)² + 3(360 - 402.5)² + 5(350 - 402.5)² + 4(390 - 402.5)²] / 16
= (87.5² + 3(117.5²) + 3(-42.5²) + 5(-52.5²) + 4(-12.5²)) / 16
= (7656.25 + 3(13806.25) + 3(1806.25) + 5(2756.25) + 4(156.25)) / 16
= (7656.25 + 41418.75 + 5418.75 + 13781.25 + 625) / 16
= 70900 / 16
= 4431.25 calories²

Finally, we can calculate the standard deviation (σ) by taking the square root of the variance.

Standard Deviation (σ) ≈ √(4431.25)
≈ 66.6 (rounded to the nearest tenth)

Therefore, the standard deviation of the given donut calories is approximately 66.6 calories.

Absolutely! To find the standard deviation, you will need to follow these steps:

1. Calculate the mean (average) of the set of data.
- To do this, add up all the calorie values and divide by the total number of types of donuts.

2. Calculate the squared differences between each value and the mean.
- Take each calorie value and subtract the mean, and then square the result for each type of donut.

3. Calculate the variance.
- Add up all the squared differences calculated in Step 2 and divide by the total number of types of donuts.

4. Calculate the standard deviation.
- Take the square root of the variance calculated in Step 3 to get the standard deviation.

Now let's apply these steps to find the standard deviation for the given donut calorie data.

Step 1: Calculate the mean:
- Add up all the calorie values:
1(490) + 3(520) + 3(360) + 5(350) + 4(390) = 490 + 1560 + 1080 + 1750 + 1560 = 6440
- Divide by the total number of types of donuts (1 + 3 + 3 + 5 + 4 = 16):
6440 / 16 = 402.5

Step 2: Calculate the squared differences:
- For each type of donut, subtract the mean from its calorie value and square the result:
(490 - 402.5)^2 = 71722.5 (1 type)
(520 - 402.5)^2 = 138022.5 (3 types)
(360 - 402.5)^2 = 17822.5 (3 types)
(350 - 402.5)^2 = 27402.5 (5 types)
(390 - 402.5)^2 = 154.5 (4 types)

Step 3: Calculate the variance:
- Add up all the squared differences:
71722.5 + 138022.5 + 17822.5 + 27402.5 + 154.5 = 253124
- Divide by the total number of types of donuts (16):
253124 / 16 = 15820.25

Step 4: Calculate the standard deviation:
- Take the square root of the variance:
sqrt(15820.25) ≈ 125.75

Rounded to the nearest 10th, the standard deviation of the donut calorie data is approximately 125.8.

add: 490 + 3(520) + 3(360) + 5(350) + 4(390) , then divide by 16

this will be your average or mean (I had 402.5)
now for each data value, take (mean - number), square it then add up those squares
e.g. for the 350 : 402.5-350 = 52.5
52.5^2 = 2756.25 <--- you will have 5 of those, so just multiply it by 5

add up those 16 squares
divide by 16, then take the square root

let me know what you got