Case Study: MBA Schools in Asia-Pacific
Statistics Concepts and Descriptive Measures
Purpose of Assignment
The purpose of this assignment to orient students to the key concepts in statistics. This assignment will introduce students to the language of statistics. Students will also get a chance to warm-up on evaluating some basic descriptive statistics using Excel® prior to the course start.
Assignment Steps
This assignment has an Excel® dataset spreadsheet attached. You will be required to only do one of the three datasets.
Resource: Microsoft Excel®, Statistics Concepts and Descriptive Measures Data Set
Download the Statistics Concepts and Descriptive Measures Data Set.
Choose one of the following datasets to complete this assignment:
Consumer Food
Financial
Hospital
Answer each of the following in a total of 90 words:
For each column, identify whether the data is qualitative or quantitative.
Identify the level of measurement for the data in each column.
For each column containing quantitative data:
Evaluate the mean and median
Interpret the mean and median in plain non-technical terms
Use the Excel =AVERAGE function to find the mean
Use the Excel =MEDIAN function to find the median
For each column containing quantitative data:
Evaluate the standard deviation and range
Interpret the standard deviation and range in plain non-technical terms
Use the Excel =STDEV.S function to find the standard deviation
For range (maximum value minus the minimum value), find the maximum value using the Excel =MAX function and find the minimum value using the Excel's =MIN function
For each column, identify whether the data is qualitative or quantitative
Quantitative data is numerical data. Mathematical operations can be performed on quantitative data. On the other hand, qualitative data is concerned with description. Mathematical operations cannot be performed on qualitative data. There are five columns in this data set.
Annual Food Spending: Quantitative data
Annual Household Income: Quantitative data
Nonmortgage household debt: Quantitative data
Region: Qualitative data. Here numbers 1, 2, 3 and 4 are used for identification purpose. Addition, subtraction, multiplication, division, and other mathematical operations cannot be performed on this data.
Location: Qualitative data. Here, numbers 1 and 2 are used for identification purpose. They are not values.
Identify the level of measurement for the data in each column.
S. S. Stevens proposed four levels of measurement: nominal, ordinal, interval, and ratio. (Salkind, 2012) Nominal measurements are only names which are different from one another. There is no ordering meaning of attributes. The ordinal measurement allows for rank order, but it does not allow for relative degree of differences between two data. The interval measurement allows relative degree of difference between two data, but does not allow the ratio between two data. Ratio measurement allows ratio between two data.
The level of measurement for the data in each column is as follows:
Annual Food Spending: Ratio
Annual Household Income: Ratio
Nonmortgage household debt: Ratio
Region: Qualitative data. Nominal
Location: Qualitative data. Nominal
For each column containing quantitative data:
Evaluate the mean and median
Interpret the mean and median in plain non-technical terms
Use the Excel =AVERAGE function to find the mean
Use the Excel =MEDIAN function to find the median
Annual Food Spending:
Mean: $8,996
Median: $8,932
The mean value is the average value. The median value is the middle value in the list if numbers are arranged in ascending or descending order. The average annual food spending on consumer food is $8,996. Half of the people spend more than $8,932 and half of the people spend less than $8,932 on consumer food.
Annual Household Income
Mean: $55,552
Median: $54,957
The average annual household income is $55,552. Half of the household earn less than $54,957 and half of the household earn more than $54,957 per year.
Nonmortgage household debt
Mean: $15,604
Median: $16,100
Average nonmortgage household debt is $15,604. Half of the households have more than $16,100 nonmortgage household debt and half of the households have less than $16,100 nonmortgage household debt.
For each column containing quantitative data:
Evaluate the standard deviation and range
Interpret the standard deviation and range in plain non-technical terms
Use the Excel =STDEV.S function to find the standard deviation
For range (maximum value minus the minimum value), find the maximum value using the Excel =MAX function and find the minimum value using the Excel's =MIN function
Annual Food Spending:
Standard Deviation: 3,125.01
Range: 15,153
Standard deviation measures how spread out numbers are. Low standard deviation shows that data points tend to be close to the mean, while a high standard deviation shows that data points are spread out over a wide range of values, farther from mean. Here, data points are close to the mean annual food spending of $8,996.
Range is an estimate of the spread of data. The annual food spending data is not wide spread.
Annual Household Income
Standard Deviation: 14,661.36
Range: 74,486
The data points are spread over a wide range of values from mean annual household income of $55,552. This reflects from moderately high range value of 74,486 also.
Nonmortgage household debt
Standard Deviation: 8,583.54
Range: 36,374
The data points are spread over a wide range of values from mean nonmortgage household debt of $15,604. The standard deviation value is more than half of the mean value. This reflects from very high range value of 36,374. This indicates that minimum and maximum nonmortgage household debts are separated by $36,374, which is very high.
References
Salkind, N. J. (2012). Exploring Research. (5th ed.). Pearson Prentice Hall.
