Summary Statistics: Measures of Center

A group of diners were asked how much they would pay for a breakfast in dollars. Their responses were:

1. Find the mean, including units.

2. Find the median, including units.

3. Based on the mean and the median, would you expect the distribution to be symmetric, skewed left, or skewed right? Explain.

The amount of commercials in an hour of television varies by channel. The total length (in minutes) of all commercials from 8 pm to 9 pm for some randomly selected broadcast and cable channels on a weekday evening were:

1. Find the mean, inluding units.

2. Find the median, including units.

3. Based on the mean and median, would you expect the distribution to be symmetric, skewed left, or skewed right?

You recorded the time in seconds it took for 8 participants to solve a puzzle. The times were:

1. Find the mean, including units.

2. Find the median, including units.

3. Based on the mean and the median, would you expect the distribution to be symmetric, skewed left, or skewed right? Explain.

You weigh 9 Oreo cookies, and you find the weights (in grams) are:

1. Find the mean, including units.

2. Find the median, including units.

3. Based on the mean and the median, would you expect the distribution to be symmetric, skewed left, or skewed right? Explain.

Use the following table is the cost of purchasing a car at a local dealership. Some of the cars sold were new and some were used.

1. Calculate find the mean, including units.

2. Can you figure out how to find the median using the frequency table? See if you can do it without listing out all the data values.

3. Based on the mean and the median, would you expect the distribution to be symmetric skewed left or s…

As part of a study of email, a researcher counted the length of 34 emails. The lengths of the emails are shown below, rounded to the nearest thousand characters (so a length 0 means that the numbers of characters rounded to 0, not that the message was blank).

1. Calculate and find the mean, including units.

2. Can you figure out how to find the median using the frequency table? See if you can do it withou…

Studies are often done by pharmaceutical companies to determine the effectiveness of a treatment. Suppose that a new cancer drug is currently under study. Of interest is the average length of time in months patients live once starting the treatment. Two researchers each follow a different set of 40 cancer patients throughout their treatment. The following data (in months) are collected.

Researcher…

The US Census Bureau, in addition to counting the population of the US every 10 years, conducts yearly informational surveys, such as the American Community Survey (ACS). For the 2012 ACS, a randomly chosen group of 20 respondents (10 males, 10 females) answered a question about their incomes.

Income in dollars for people who identify as female:

Income in dollars for people who identify as male:

1. Find…

Make up three data sets with 5 values each that have:

1. The same mean but different medians

2. The same median but different means.

The frequency table below shows the number of women's shoes that were sold in an hour at a local shoe store.

1. Would you treat this data as categorical or quantitative?

2. How would the bar graph be different from the histogram?

3. Treat the data as quantitative and find the mean and the median. Are these useful statistics?

For each of the following distributions, would you expect that the mean is less than the median, greater than the median, or approximately equal to the median? Explain your reasoning.

1. Household incomes in the US

2. Weights of newborn babies born at term

3. The number of children in a household in the US

4. Medical costs for all adults

5. Medical costs for adults in the US older than 65