H3.1

In a​ symmetric, unimodal​ distribution, about​ two-thirds of the observations are​ where?

Approximately​ two-thirds of the observations in a​ symmetric, unimodal distribution are within one standard deviation of the mean.

A sociologist​ says, "Typically, men in a certain country still earn more than​ women." What does this statement​ mean?

In a distribution of​ values, the typical value is given by the mean. In this​ case, the average salary of a man is higher than that of a​ woman, so when comparing the distribution of​ men's salaries to​ women's salaries, the center of the distribution for men is greater than the center of the distribution for the women.

Suppose you have a data set with the weights of all members of a high school soccer team and all members of a high school academic decathlon team​ (a team of students selected because they often answer quiz questions​ correctly). Which team do you think would have a larger standard deviation of​ weights? Explain.

The academic decathlon team would have a larger standard deviation of weights. Academics​ don't require a specific weight to​ succeed, so the distribution of weights should mirror that of the general population.

The​ ____ is another term for the arithmetic average

The mean is another term for the arithmatic average. It can be thought of as the balancing point of a distribution of data.

The mean of a collection of data is located at the​ ______ of a distribution of data.

The mean of a collection of data is located at the​ "balancing point" of a distribution of data.

The mean represents the typical value in a set of data for what type of​ distribution?

The mean represents the typical value in a set of data for distributions that are roughly symmetric.

The​ ______ is a number that measures how far away the typical observation is from the mean.

The standard deviation is a number that measures how far away the typical observation is from the mean. For most​ distributions, a majority of observations are within one standard deviation of the mean value.

A real estate agent claims that all things being​ equal, houses with swimming pools tend to sell for less than those without swimming pools. What does this statement​ mean?

The typical price for homes with pools is smaller than the typical price for homes without pools.