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.

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 case, to find the mean weight of the turkeys, you would add all the weights together and divide by the number of turkeys in the sample.

Variance

Variance measures the spread of a set of values around the mean. It is calculated by taking the average of the squared differences between each value and the mean. A higher variance indicates that the weights of the turkeys are more spread out from the mean, while a lower variance suggests they are closer to the mean.

Standard Deviation

Standard deviation is the square root of the variance and provides a measure of the average distance of each data point from the mean. It is a useful statistic for understanding the dispersion of weights in the sample of turkeys, with a smaller standard deviation indicating that the weights are closely clustered around the mean.