Hans Lienesch is known as the Ramen Rater and has rated thousands of varieties of instant noodles on his website (theramenrater.com). The data set found in our StatCrunch Group presents 2095 different varieties, styles, and ratings of Ramen. The data set is called “Ramen Ratings.”
a) Use StatCrunch to create a one-way table for the variable “Country/Region” using both counts and percentages. Select Stat Tables Frequency. Select “Country/Region” in the Select Column(s) box, and select both ‘Frequency’ and ‘Percent of total’ in the Statistic(s) box by holding down the Ctrl Key (Command Key on Macs) when making these selections. Copy your table into your document and then manually round the values in the ‘Percent of total” column to two decimal places in the StatCrunch table that you have copied into your document.
b) Interpret your findings from the table in 1(a) by identifying the country/region with the largest and smallest percentage. Use complete sentences with context and include the country/region and percentage in the sentences.
c) Use StatCrunch to generate a two-way table for the variables “Country/Region” and “Style”. Go to Stat Tables Contingency With Data (since you have the raw data in StatCrunch). Select “Country/Region” as your row variable and “Style” as your column variable. Lastly, unclick (or deselect) “Chi-Square test for independence” since it is highlighted by default by holding the Ctrl key and clicking on it. Copy your table into your document.
d) Calculate the combination of variables with the largest and smallest percent of the total (2095) in regards to both “Country/Region” and “Style.” Provide both the label and the percentage and answer this question in two complete sentences.
e) What values are the same when looking at both your one-way table and your two-way table? Be specific if referencing rows or columns.
f) Now, create two more two-way tables keeping “Country/Region” as your row variable and “Style” as your column variable. One table needs to include row percentages and the other needs to include column percentages. To do this, select row percent in the display box to for the first table and column percent for the second table. Include both tables in your document.
g) Specifically interpret the meaning of the row percentage found in the “Japan” and “Pack” cell. Note that there are 225 observations in that cell.
h) Now, specifically interpret the meaning of the column percentage found in the “Japan” and “Pack” cell. Note that there are 225 observations in that cell.
Let us analyze the distribution of countries of origin of the ramen noodles that received five star ratings. Use the “Five Star Ramen Ratings” data set posted in our StatCrunch group to answer the following questions.
a) Using the variable named “Country/Region”, produce a relative frequency bar chart using Graph Bar Plot With Data. Please properly label axes and provide a meaningful title and copy it into your document.
b) Using the variable “Country/Region”, produce a relative frequency Pareto chart. Begin with your bar chart, and edit it by changing “Order by” to Count Descending. Properly title and label your graph and copy it into your document.
c) Using the variable “Country/Region”, produce a Pie Chart using Graph Pie Chart With Data. Add an appropriate title and copy this entire graph including the legend into your document.
d) Use the three graphs to answer the question: Which country/region of origin earned the most five star ratings? Present both the count and the proportion and write your answer in one sentence.
e) Now produce a grouped relative frequency bar chart (to copy to your document) by following the directions below. Continue to use the Five Star Ramen Ratings data set.
Go to Graph Bar Plot With Data.
For this grouped bar chart, graph the variable “Style” and group by “Country/Region.” To “group by” click the arrow next to Group by box (the third box down) and select the variable you are asked to group by. In the Type box (5th box down from the top) choose relative frequency within category. Title this graph clearly. You may keep the default labels for the x and y-axis.
f) For this next grouped bar chart, graph the variable “Country/Region” and group by “Style.” In the Type box (5th box down from the top) choose relative frequency within category. Title this graph clearly. You may keep the default labels for the x and y-axis.
g) The two graphs you made in 2(e) and 2(f) are another representation of row and column percentage two-way tables. If we consider the row variable to be “Country/Region” and the column variable to be “Style,” which graph would correspond to a row percentage two-way table and which graph would correspond to the column percentage two-way table? Answer in two complete sentences. You may create these two-way tables for this data set to help you answer the questions, but the tables do not need to be copied into your solutions document.
A number of variables concerning the population of the states of the United States are presented in the “State Population Information” data set posted in StatCrunch. The “Density” variable is measured as people per square mile.
a) Create a relative frequency histogram for the variable “Density” by using Graph Histogram. Properly title and label your graph and copy it into your document.
b) Interpret the shape of this distribution in one complete sentence.
c) Use StatCrunch to obtain the sample size (n), mean, and standard deviation for the “Density” variable by using Stat Summary Stats Columns. Note: in the Statistics box, select the summary statistics listed above in the exact order given. Copy the entire table into your document and manually round each value to two decimal places when necessary.
d) Use StatCrunch to obtain the five number summary and the IQR for the “Density” variable (the five number summary includes Min, Q1, Median, Q3, Max). Go to Stat Summary Stats Columns to obtain these values. Note: in the Statistics box, select the summary statistics listed above in the exact order given. Copy the entire table into your document.
e) Choose the appropriate summary statistics for center and spread (presented in either 3(c) or 3(d)) based on your stated shape of the distribution in 3(b).
f) Use your summary statistics from part 3(d) and determine the fences used to mathematically identify outliers for the “Density” variable. To do this, type all steps in your calculations manually, including how you obtained the upper and lower fences.
g) Construct a horizontally oriented boxplot of the “Density” variable by using Graph Boxplot. To do this, click the “Draw boxes horizontally” box. Properly title and label and copy this graph into your document.
h) How many outliers do you identify (please use both the boxplot and your results from 3(f) to answer this question)? Hint: you can sort your data by “Density” (using Data Sort in StatCrunch) to get the correct number or hover your cursor over the boxplot. Write your response in a complete sentence.
i) List the three largest outliers in one complete sentence. Include the state and the actual density measurement in your answer.
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