Question

You come from a large, dysfunctional family. You learn of this year’s upcoming reunion, and dread the very thought of being around those people for any length of time. However, you’ve been intrigued by your introductory statistics course, and decide you will have some fun with the reunion by using it as an opportunity to study your family. As a preliminary project, you want to keep track of how many times each family member verbally assaults another person throughout the first 24 hours.

After 24 hours, you review your notes:
Family Member # Verbal Assaults
Stew (Dad) 5
Marge (Mom) 7
Betsy 18
Fred 11
Gracie 4
Jorge 10
Kim 5
Ferdinand 15
Hal 6
You 19
Find the mean, median, and mode of your distribution:
1. Mean
2. Median
3. Mode
4. Which measure of central tendency do you think is most appropriate for this dataser? Why?
5. What is the range of your dataset? Show how you figured it out.
6. Define, as specifically as necessary, the population in which you are interested for this research. In other words, how do you decide whether a person would be appropriate to include in your study?
7-9. Find the standard deviation for the data in the table on the first page. Showing your work is how you earn points for this part
10. What is the standard deviation of your dataset?

Answer 1

Explained below.

Explanation:

The data provided is for the number of times each family member verbally assaults another person throughout the first 24 hours.

Use Minitab to compute the descriptive statistics.

Go to Stat → Basic Statistics → Display Basic Statistics

A dialog box will open.

Select the variable.

Select 'Statistics'.

Another dialog box will open.

Select the statistics required.

Press OK.

Select "Graphs'.

Select Histogram.

Press OK

The output is attached below.

(1)

The mean of the data is, Mean = 10.

(2)

The median of the data is, Median = 8.50.

(3)

The mode of the data is, Mode = 5.

(4)

The inequality statement for the mean, median and mode is:

Mean > Median > Mode

A distribution is known as to be skewed to the right, or positively skewed, when maximum of the data are collected on the left of the histogram of the distribution.

Also if the Mean > Median > Mode then the distribution is skewed to the right.

For a skewed distribution the best of central tendency is the median.

So, the measure of central tendency that is most appropriate for this dataset is, Median = 8.50.

(5)

The range of the data set is:

Range = Maximum - Minimum

= 19 - 4

= 15

Thus, the range is 15.

(6)

The population of interest is the number of times the family members verbally assaults another person throughout the first 24 hours.

(7)

Consider the Minitab output.

The standard deviation of the data set is, SD = 5.60.