Intro to Descriptive Statistics

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Kean University *

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Statistics

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Feb 20, 2024

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Shaunna Smith MGS-2150 Professor Chaudhuri Introduction to Descriptive Statistics Define descriptive and inferential statistics. Focus on the difference between the two types of approach. Descriptive statistics summarizes or describes the characteristics of a data set. Descriptive statistics uses three different categories of measurements, which are the measure of central tendency, or mean, mode, and ratio. The measure of variability, for example, would be the standard deviation. The last category of measurement used in descriptive statistics is the frequency of distribution or the count of a data set. Inferential statistics is when you conclude and make predictions based on the data. If you wanted to know how many high school seniors would attend college, you could use inferential statistics to take a sample of 10 high school seniors and use the information, or data from them to predict how many will attend college in the fall. The difference between the two types of approaches is inferential is more about taking a handful of data and using it to predict or forecast a hypothesis of a larger population. Descriptive statistics is taking all the data from a larger population using averages of sales or products and making a data set that is informational not a hypothesis. An example to showcase the difference between the two would be making a new ketchup recipe, the group who wants to make the ketchup recipe gathers all the data, average sales, average transactions, and average cost. They gather all the data and use it to roll out the new ketchup recipe this would be an example of descriptive statistics. The other group using inferential statistics is doing the same thing but instead of using all the data for informational purposes, they use it to predict or forecast the number of sales that will happen with the new ketchup recipe. Define population and sample. List typical parameters from population and sample statistics. A population is an entire group of data sets. All of which share common characteristics. A sample can be defined as a subset of a population. An example of each would be the population of a classroom and the sample would be the Top 5 students in the classroom. In the population, the entire classroom shares a common characteristic of being in the same class. While the sample or subset is they are still in the same class but are the highest achieving students in their class. Typical parameters from population are the numerical value that describes the population, is it a whole country or just a state? It must be calculated for the entire population, ex. New Jersey. It must have a purpose and have precision and accuracy. Precision and accuracy in a population parameter would be more accurate than sample statistics could be. Greek letters are

used in population for the mean a Greek letter ( μ ) is used. An example would be the income of the population of New Jersey. As for sample statistics, a numerical value is used as well, but the numerical value is used from a population sample. An example would be only people living in Union could be a part of the sample statistic. Its purpose is to estimate the population parameters. Although the parameters of the population are more accurate, sample statistics are far less accurate and could be less precise. The notation used in sample statistics is Roman letters like x̄ for the sample mean or average. Refer to Table 1.6 (textbook) and indicate the types of variables and the scale of measurement for each variable. In the data set of Table 1.6, there are five variables. The variables are as follows, operating system and CPU manufacturer are qualitative. The operating system is measured on a nominal scale. CPU manufacturer is measured on a nominal scale. While battery life, cost, and display size are quantitative. Battery life is continuous and measured on a ratio scale. Cost is continuous and measured on a ratio scale. Display size is also continuous and measured on a ratio scale. Refer to Table 1.6 (textbook) and indicate how you can summarize the information in each variable. To effectively summarize the information for each variable can be difficult if there are a lot of different elements in the data set. For this Table 1.6 there are only 10 different element names and five different variables, all of which can easily be summarized. All the variables, cost, operating system, CPU manufacturer, battery life, and display size can be summarized by the central tendency of either standard deviation or its mode and or mean of the information given in the data set of Table 1.6.

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