Calculate the mean, variance, and standard deviation for a sample of turkeys weighed at 8 weeks of age that have the following weights in ounces:
161, 172, 155, 173, 149, 177, 156, 174, 158, 162, 171, 181.

Verified step by step guidance

1. Step 1: Calculate the mean (average) weight. Add all the weights together and divide by the total number of weights. Use the formula: $\mathrm{Mean}=\frac{\sum x}{n}$, where $\sum x$ is the sum of all weights and $n$ is the number of weights.
2. Step 2: Calculate the variance. First, find the squared difference between each weight and the mean. Then, sum these squared differences and divide by the total number of weights minus one (since this is a sample). Use the formula: $\mathrm{Variance}=\frac{\sum {\left(}^x}{n}$.
3. Step 3: Calculate the standard deviation. Take the square root of the variance. Use the formula: $\mathrm{Standard}\mathrm{Deviation}=\sqrt{\mathrm{Variance}}$.
4. Step 4: Verify your calculations by double-checking the sum of weights, the mean, and the squared differences to ensure accuracy.
5. Step 5: Interpret the results. The mean represents the average weight of the turkeys, the variance indicates the spread of the weights, and the standard deviation provides a measure of how much the weights deviate from the mean on average.

Key Concepts

Mean

The mean is the average value of a set of numbers, calculated by summing all the values and dividing by the total number of values. In this context, it represents the average weight of the turkeys at 8 weeks of age, providing a central value around which the weights are distributed.

Variance

Variance measures the degree of spread in a set of values, indicating how much the individual weights differ from the mean. It is calculated by averaging the squared differences between each weight and the mean, providing insight into the consistency of the weights among the turkeys.

Standard Deviation

Standard deviation is the square root of the variance and provides a measure of the average distance of each weight from the mean. It is a key statistic that helps to understand the variability of the weights, with a lower standard deviation indicating that the weights are closely clustered around the mean.