The data below represents the amount of grams of carbohydrates in a sample serving of breakfast cereal.
10 18 24 30 19 22 24 20 18 25 20 22 19
The variance for this data would be __________ grams.
To find the variance for this data, we need to follow these steps:
1. Calculate the mean (average) of the data.
2. Subtract the mean from each data point and square the result.
3. Calculate the mean of the squared differences.
Let's go through the steps to find the variance:
Step 1: Calculate the mean.
To find the mean, add up all the data points and divide by the number of data points.
10 + 18 + 24 + 30 + 19 + 22 + 24 + 20 + 18 + 25 + 20 + 22 + 19 = 271
There are 13 data points, so:
Mean = 271/13 = 20.85 (rounded to two decimal places)
Step 2: Subtract the mean from each data point and square the result.
Subtract the mean from each data point and square the result:
(10 - 20.85)^2 = 125.0225
(18 - 20.85)^2 = 7.2025
(24 - 20.85)^2 = 10.1025
(30 - 20.85)^2 = 85.1025
(19 - 20.85)^2 = 3.4225
(22 - 20.85)^2 = 1.3725
(24 - 20.85)^2 = 10.1025
(20 - 20.85)^2 = 0.7225
(18 - 20.85)^2 = 7.2025
(25 - 20.85)^2 = 17.3025
(20 - 20.85)^2 = 0.7225
(22 - 20.85)^2 = 1.3725
(19 - 20.85)^2 = 3.4225
Step 3: Calculate the mean of the squared differences.
Add up all the squared differences and divide by the number of data points.
125.0225 + 7.2025 + 10.1025 + 85.1025 + 3.4225 + 1.3725 + 10.1025 + 0.7225 + 7.2025 + 17.3025 + 0.7225 + 1.3725 + 3.4225 = 273.1400
There are 13 data points, so:
Variance = 273.1400/13 ≈ 21.01 grams
Therefore, the variance for this data is approximately 21.01 grams.
I recommend using your calculator. I calculated sigma(n-1) as a sample, and got 4.705, making variance(sample)=22.14
You may not be wanting sample standard deviation and variance. Use your calculator.