# Descriptive Statistics : Mean, Median, Mode and Standard Deviation

Please see the attached file for the fully formatted problems.

Unit 9: Critical Thinking Exercise

Data Collection and Data Analysis

The Tastee-Yummy Dog Bone Company has developed four new commercials for their line of flavored dog cookies. Before selecting one of the commercials for production, they conducted research to assess the target audience's reactions to each commercial as well as their reactions to specific product claims communicated by the commercials.

Mall-intercept interviews were conducted to collect the data. Individuals walking through the mall were screened and those in the target audience who agreed to participate in the research were taken to an interviewing area and shown three commercials. After viewing all three commercials, a twenty-minute survey was conducted to tap the key goals of the study. Among the items that were included in the survey were the following:

1. Gender

a. Male (1)

b. Female (2)

2. What is your age to the nearest whole year? _____

3. Now that you have seen the commercials for Tastee-Yummy Dog Cookies, please rate each statement below on a scale of 1 (Strongly Disagree) to 5 (Strongly Agree).

a. My dog would like the advertised treats better than the brand I am currently buying.

Strongly Disagree Disagree Neutral Agree Strongly Agree

1 2 3 4 5

b. My dog would be better behaved if I used the advertised treats as a reward for good behavior.

Strongly Disagree Disagree Neutral Agree Strongly Agree

1 2 3 4 5

4. The commercials discussed several benefits of Tastee-Yummy Dog Cookies. Please indicate the relative importance of these benefits to you and your dog by assigning points to each benefit. You have 100 points to distribute among the following four benefits. You can give as few or as many point, or even no points, to each benefit. The more points that you give to a specific benefit the more important you feel that benefit is. Fewer points indicate less importance. Please make sure that you use all 100 points.

a. Clean teeth ____

b. Prevents tooth decay ____

c. Freshens breath ____

d. Provides added nutrition ____

TOTAL: 100

5. The names of the four commercials are listed below. Please rank the commercials to reflect how well you liked them. Place a "1" next to the commercial that you liked the best, a "2" next to the commercial you liked next best, a "3" to the next commercial that you liked the best, and finally a "4" to the commercial you liked the least. Please use each number only once.

a. Dog's Day Out ____

b. Nine Yards ____

c. Couch Dog ____

d. Teeth of My Dreams ____

The responses to fifty individuals in the sample are shown below. Use this data and your knowledge of the relationship between levels of measurement and levels of analysis to address the following issues.

Q1. Gender

At what level of measurement is this question? What are the characteristics of the sample in terms of gender? Which measure of central tendency (mean, media or mode) best describes this characteristic? Why is this measure the most appropriate? Is it appropriate to calculate variance and standard deviation? Why or why not? Present the results of your analysis in both tabular and pictorial (bar graph) formats.

Q2. Age

At what level of measurement is this question? Group the data to determine the characteristics of the sample in terms of age. Which measure of central tendency (mean, median or mode) best describes the characteristic? Why is this measure the most appropriate? Is it appropriate to calculate variance and standard deviation? Why or why not? Present the results of your analysis in both tabular and pictorial (bar graph) formats.

Q3. Product Appeal

At what level of measurement are these two questions? Using the data from Q3, determine the extent to which the product appeals to the target audience. How does each measure of central tendency help you to understand the characteristics of the distribution? What measure do you believe is the most appropriate for illustrating the level of product appeal? Is the calculation of variance or standard deviation appropriate? Why or why not?

Q4. Product Benefits

At what level of measurement is this question? When you present the results of the research, your client at Tastee-Yummy will ask for your recommendations as to which product benefit should receive the most emphasis in the advertising campaign. Based on the data collected (below), which benefit would you recommend? On what basis do you make this recommendation? What descriptive measures are most appropriate for describing the characteristics of the distribution and for helping you to identify the most appropriate benefit? Present the results of your analysis in both tabular and pictorial (bar graph) formats.

Q5. Commercial Liking

At what level of measurement is this question? The client at Tastee-Yummy loves the fourth commercial, "Teeth of My Dreams." The client has every expectation that others in the target audience will love this commercial also and that, at least in part due to this very high liking, the agency will recommend this commercial for production. Is the client correct? Does the target audience love this commercial? Do they even like the commercial? What descriptive measures are appropriate for describing the characteristics of the distribution and for helping you identify the commercial that is best liked by the target audience? Present the results of your analysis in both tabular and pictorial (bar graph) formats.

Data for Tastee-Yummy Dog Cookie Research

We are using a set of data to calculate means, medians, modes and are also asked to determine whether computing the standard deviation is of any use, and if so, how so.

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#### Solution Summary

Mean, Median, Mode and Standard Deviation are investigated. The solution is detailed and well presented.