# Analyze the data on burrito weights using descriptive statistical measures such as the mean and standard deviation, and tools such as a frequency distribution and a histogram.

Information for paper:

Rapido Burrito is a small, regional chain of quick service restaurants. Rather than wait in a cafeteria-style line, customers check boxes for their choice of ingredients, sauce, and so on paper menus at their table. The food is prepared quickly and then delivered to the tables.

Lately, one of the store managers has been hearing customer complaints, such as: “The tortillas are too thin”; “The food is not hot”; “Every time I get a burrito, it seems to be a different size”; and “I got the wrong ingredients on my burrito.” Many complaints were submitted through the corporate website.

The district manager was most concerned with the comments about the consistency of size. One of the staff designed a customer survey using the questions below, based on a 5-point Likert scale (5=excellent, or strongly agree; 1= poor or strongly disagree) for the first 10 questions. The last two questions were coded as a 1, 2, 3, or 4.

Customer Survey Questions:

Was the menu easy to read?

Was the order prepared correctly?

Was the food tasty?

Was the food served hot?

Were employees courteous and polite?

Was the restaurant clean?

In your opinion, did you receive a good value for the price you paid?

What was your level of satisfaction?

How likely are you to dine with us again?

How likely are you to recommend us to your friends/family?

How often do you eat at Rapido Burrito? First time, less than once/month, one to three times a month, weekly?

What was the main ingredient in your burrito: chicken, beef, pork, or beans?

They administered the questionnaire to 25 random customers. The restaurant also gathered data on the weights of 50 samples of 3 burritos (a total of 150). Both the survey data and weight data are available on the Excel worksheet Rapido Burrito Case Data included in Week 1 of this course.

Case Questions:

What conclusions do you reach when you calculate descriiptive statistics for the answers to each of the survey questions in the database?

If you average the responses to the first seven questions by customer, how closely are those averages correlated to the satisfaction score? Include a scatter chart in your analysis.

Analyze the data on burrito weights using descriiptive statistical measures such as the mean and standard deviation, and tools such as a frequency distribution and a histogram. What do your results tell you about the consistency of the food servings?

What recommendations for decision making and improvement can you make to the store manager?

Let’s assume we have collected data on burrito weights from a local restaurant, and we have the following weights (in ounces) for 50 burritos:

6.5, 7.2, 7.5, 7.8, 8.1, 8.2, 8.3, 8.5, 8.6, 8.6, 8.8, 8.9, 9.0, 9.2, 9.3, 9.5, 9.6, 9.7, 9.8, 9.8,

9.9, 10.0, 10.1, 10.2, 10.3, 10.4, 10.5, 10.5, 10.6, 10.7, 10.7, 10.8, 11.0, 11.1, 11.2, 11.3, 11.4, 11.5,

11.6, 11.7, 11.8, 12.0, 12.1, 12.2, 12.3, 12.5, 12.7, 13.0, 13.1, 13.5

Descriptive statistical

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Mean: The mean is a measure of central tendency that represents the average weight of the burritos. We can calculate the mean by adding up all the weights and dividing by the total number of burritos.

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Mean = (6.5 + 7.2 + … + 13.5) / 50 = 9.98 ounces

Standard deviation: The standard deviation is a measure of the spread of the data. We can calculate the standard deviation by finding the square root of the variance, which is the average of the squared differences from the mean.

scss

Variance = [(6.5 – 9.98)^2 + (7.2 – 9.98)^2 + … + (13.5 – 9.98)^2] / 50 = 4.43

Standard deviation = sqrt(Variance) = 2.10 ounces

Tools:

Frequency distribution: A frequency distribution is a table that shows how often each weight occurs in the data set. We can create a frequency distribution by grouping the weights into intervals and counting the number of burritos in each interval.

sql

Weight Interval | Frequency

—————-|———–

6.0 – 7.9 | 4

8.0 – 9.9 | 18

10.0 – 11.9 | 19

12.0 – 13.9 | 9

Histogram: A histogram is a graphical representation of the frequency distribution, where each interval is represented by a bar with a height equal to the frequency of the interval.