Summarizing quantitative data #1 - Questions and Answers

Question 1 Tell, please, what’s the difference between the “population of interest” and “parameter of interest”? Answer 1 The population is a group of interest, such as the people who filled out a recent survey. The parameter is the descriptive measure of that population. Answer 2 The parameter is the number/object you wish to estimate, and the population is a group of individuals to which that parameter describes. Question 2 The manager at Publix recently received information that customer satisfaction dropped at noon due to overcrowding in the checkout aisle. As a result, the manager went to the main floor to record the number of customers waiting in aisles 1–10 at noon. Which of the following choices would be an accurate description of the way the “number of customers” is used in this data set? a. individuals for the data set b. continuous qualitative variable for this data set c. discrete qualitative variable for this data set d. qualitative variable for this set e. continuous quantitative variable for this data set f. discrete quantitative variable for this data set Answer Step 1: The manager at Publix recently received information that customer satisfaction dropped at noon due to overcrowding in the checkout aisle. As a result, the manager went to the main floor to record the number of customers waiting in aisles 1–10 at noon. Step 2: An accurate description of the way the “number of customers” is used in this data set is given as: f. discrete quantitative variable for this data set. As the result, the manager went to the main floor to record the number of customers waiting in aisles 1–10 at noon, which is quantitative and discrete in nature. Step 3: Therefore, an accurate description of the way the “number of customers” is used in this data set is given as: f. discrete quantitative variable for this data set. Question 3 Forecasting Forecasting is important relative to capacity requirements planning. What are some of the merits of using judgment methods (i.e., qualitative data) in contrast to quantitative forecasting methods? Which methods are considered to be superior or more accurate, and in what forecast situations would require judgment methods? In what situations would require a quantitative approach to forecasting? Answer Techniques for qualitative data forecasting primarily describe the traits and qualities of the data. Data is primarily gathered through questionnaires, observations, interviews, and feedback. A qualitative technique is a process that relies on expert judgment rather than mathematical methods when making future predictions. In order to predict future outcomes, qualitative forecasting techniques rely on the opinions and suggestions of highly qualified and experienced professionals. Quantitative data is used when the researcher has to struggle with the quantity problem. Quantitative data are countable in number and can be measured through scale and other instruments. Statistical Package for Social Science (SPSS), statistical analysis software is used to analyze the quantitative data. The merits of Qualitative data over the Quantitative data will be analyzed through the following points. Enriching: It became easier to find issues in data using the qualitative data approach rather than a quantitative approach. Examining: Data and information generated from qualitative research can be tested using the quantitative approach. Explaining: Qualitative data is more efficient and reliable to better understand the unpredictable results from the quantitative data as compared to the quantitative forecasting techniques. In addition to the advantages listed above, using qualitative forecasting techniques over quantitative ones allows businesses to more easily understand consumer demand, purchasing patterns, and other pertinent data that is necessary for capacity requirement planning and will be sufficient to meet user needs. Quantitative forecasting techniques are more accurate and superior in nature because organizations need to estimate their business activities in numbers so that the management team can discuss the strategies, plans, and policies with the top-level management in the form of numbers. Quantitative forecasting techniques will provide the future trendline to analyze the data. A qualitative approach is most favorable in the circumstances where it is suspected that the forecasted data will deviate distinctly from the one in the past period, and which cannot be predicted by using the Quantitative approach. When data is unavailable, and if the data is available but not relevant, then in this situation, the qualitative forecasting techniques are sufficient to meet user needs. Quantitative techniques are the statistical techniques that required mathematical calculations to make future predictions. This method is applied when numerical data of the past is available. Question 4 Explain which measure of spread would best describe the payroll: the range, the IQR, or the standard deviation. Answer 1 Inter quartile range: In contrast to the range, which measures only differences between the extremes, the inter quartile range (also called mid spread) is the difference between the third quartile and the first quartile. Thus, it represents the width in the middle 50 percent of the data and unlike the range, it is not affected by extreme values. IQR = 𝑄 3 − 𝑄 1 IQR=Q 3 ​ −Q 1 ​ Here, the range and the standard deviation affects by the two higher salaries, whereas the interquartile range is not affected by the higher salaries. Thus, the IQR is the measure of spread that best describe the payroll distribution. Answer 2 The measure of spread that would best describe the payroll is the standard deviation ( 𝜎 ) (σ). The standard deviation provides a measure of the average amount by which data points deviate from the mean. It takes into account the entire data set and considers each data point’s distance from the mean. The formula for calculating the standard deviation is as follows: 𝜎 = 1 𝑁 ∑ 𝑖 = 1 𝑁 ( 𝑥 𝑖 − 𝑥 ˉ ) 2 σ= N 1 ​ i=1 ∑ N ​ (x i ​ − x ˉ ) 2 ​ Where: 𝑁 N is the number of data points, 𝑥 𝑖 x i ​ represents each individual data point, and 𝑥 ˉ x ˉ denotes the mean of the data set. The range ( 𝑅 R) would not be the best measure of spread for the payroll because it only considers the difference between the maximum and minimum values and does not take into account the distribution of data points in between. The interquartile range (IQR) would be a reasonable measure of spread if the data had significant outliers. However, since we are specifically looking for the best measure of spread, the standard deviation, which considers the entire data set, is more appropriate.