Range: range  = highest score  — lowest score

Variance: the average deviation from the mean [need the SS to calculate this]

Standard Deviation: square root of the variance. A measure of the amount of variation or dispersion of a set of values.

The San Diego Wave FC is a National Women's Soccer League expansion team that began play in 2022. The team is based in San Diego, California. In their last six games they scored the following goals: 1, 6, 10, 9, 4, 6. 

Calculate the mean, variance and standard deviation for the population of N=6 

Calculate the variance and standard deviation for the following Halloween candy collected: n = 8 scores: 0, 4, 1, 3, 2, 1, 1, 0

A population has a mean of μ=80 and a standard deviation of σ=20.

1. Would a score of X=70 be considered an extreme value (out in the tail)?

2. If the standard deviation were σ=5, would a score of X-70 be considered an extreme value?

On an exam with a mean of 78, you obtain a score of X=84. Would you prefer a standard deviation of s=2 or s=10?

In an extensive study involving thousands of children, researchers found significantly higher variance in the intelligence scores for males than for females. Following are hypothetical data, similar to the results obtained in the study. Note that the scores are not regular IQ scores but have been standardized so that the entire sample has a M = 10 and a standard deviation of s = 2. 

1. Calculate the mean and the standard deviation for the sample of males and females. 

2. Based on the means and the standard deviations, describe the differences in intelligence scores for males and females. 

For the following sample of n=4 scores: 82, 88, 82 and 86: 

a. Simplify the arithmetic by first subtracting 80 points from each score to obtain a new sample of 2, 8, 2, and 6. Then compute the mean and standard deviation for the new sample. 

b. Using the values, you obtained in part a. what are the values for the mean and standard deviation for the original sample?