Describing quantitative data #2 - Questions and Answers

Question 1 True or False 1.The goal of descriptive statistics is to simplify, summarize, and organize data. 2.A summary value, usually numerical, that describes a sample is called a parameter. 3.A researcher records the average age for a group of 25 preschool children selected to participate in a research study. The average age is an example of a statistic. 4. The median is the most commonly used measure of central tendency. 5. The mode is the best way to measure central tendency for data from a nominal scale of measurement. 6.A distribution of scores and a mean of 55 and a standard deviation of 4. The variance for this distribution is 16. 7.In a distribution with a mean of M = 36 and a standard deviation of SD = 8, a score of 40 would be considered an extreme value. 8.In a distribution with a mean of M = 76 and a standard deviation of SD = 7, a score of 91 would be considered an extreme value. 9.A negative correlation means that as the X values decrease, the Y values also tend to decrease. 10.The goal of a hypothesis test is to demonstrate that the patterns observed in the sample data represent real patterns in the population and are not simply due to chance or sampling error. Answer 1 Step 1 Note: As your question have multiple questions, we have solved the first question for you. Step 2 Descriptive statistics: Descriptive statistics is mainly used to describe the given data by providing the summary statistics. The descriptive measures helps in simplifying the large data by describing the basic features of it. Both the quantitative and qualitative data can be organized by virtually displaying the and appropriate simple graphs. The descriptive statistics are used to summarize, simplify and organize data. The given statement is, "The goal of descriptive statistics is to simplify, summarize and organize data". Since, our explanation of descriptive statistics and the given statement are true, the given statement is appropriate. The given statement is True. Answer 2 The goal of descriptive statistics is to simplify, summarize, and organize data. [True] A summary value, usually numerical, that describes a sample is called a parameter. [False] A researcher records the average age for a group of 25 preschool children selected to participate in a research study. The average age is an example of a statistic. [True] The median is the most commonly used measure of central tendency. [False] The mode is the best way to measure central tendency for data from a nominal scale of measurement. [True] A distribution of scores and a mean of 55 and a standard deviation of 4. The variance for this distribution is 16. [True] In a distribution with a mean of M = 36 and a standard deviation of SD = 8, a score of 40 would be considered an extreme value. [False] In a distribution with a mean of M = 76 and a standard deviation of SD = 7, a score of 91 would be considered an extreme value. [True] A negative correlation means that as the X values decrease, the Y values also tend to decrease. [False] The goal of a hypothesis test is to demonstrate that the patterns observed in the sample data represent real patterns in the population and are not simply due to chance or sampling error. [True] Answer 3 Step 1. The goal of descriptive statistics is to simplify, summarize, and organize data. True. Descriptive statistics aims to provide a clear and concise summary of the data by using various measures, such as measures of central tendency (mean, median, mode) and measures of dispersion (variance, standard deviation). It helps in understanding the main characteristics of the data set. Step 2. A summary value, usually numerical, that describes a sample is called a parameter. False. A summary value that describes a sample is called a statistic, not a parameter. Parameters are summary values that describe a population, while statistics describe a sample. Step 3. A researcher records the average age for a group of 25 preschool children selected to participate in a research study. The average age is an example of a statistic. True. The average age recorded by the researcher for the group of 25 preschool children is an example of a statistic. It is a summary value calculated from the sample data. Step 4. The median is the most commonly used measure of central tendency. False. The median is one of the measures of central tendency, but it is not necessarily the most commonly used. The choice of measure depends on the nature of the data and the specific research question. Step 5. The mode is the best way to measure central tendency for data from a nominal scale of measurement. True. For data from a nominal scale of measurement, where the values are categories or labels without any inherent numerical value, the mode is the most appropriate measure of central tendency. It represents the category that occurs most frequently in the data set. Step 6. A distribution of scores has a mean of M = 55 and a standard deviation of SD = 4. The variance for this distribution is 16. True. The variance is equal to the square of the standard deviation. In this case, the standard deviation is SD = 4, so the variance can be calculated as SD² = 4² = 16. Step 7. In a distribution with a mean of M = 36 and a standard deviation of SD = 8, a score of 40 would be considered an extreme value. False. To determine if a score is considered an extreme value, we need to consider how far the score deviates from the mean in terms of standard deviations. In this case, the score of 40 is within one standard deviation from the mean, so it would not be considered an extreme value. Step 8. In a distribution with a mean of M = 76 and a standard deviation of SD = 7, a score of 91 would be considered an extreme value. True. To determine if a score is considered an extreme value, we need to consider how far the score deviates from the mean in terms of standard deviations. In this case, the score of 91 is more than two standard deviations above the mean, so it would be considered an extreme value. Step 9. A negative correlation means that as the X values decrease, the Y values also tend to decrease. False. A negative correlation means that as the X values increase, the Y values tend to decrease. It indicates an inverse relationship between the variables, where one variable tends to decrease as the other variable increases. Step 10. The goal of a hypothesis test is to demonstrate that the patterns observed in the sample data represent real patterns in the population and are not simply due to chance or sampling error. True. The goal of a hypothesis test is to assess whether the observed patterns or differences in the sample data are statistically significant and can be generalized to the population. It helps in determining whether the patterns are likely to be real and not just due to random chance or sampling error. Question 2 Which kind of graph or statistical data would be most useful in figuring out whether the initial characteristics of a study group are evenly distributed? A) A bar chart B) Descriptive statistic C) A box-whisker plot D) A flow chart Answer Step 1 A type of graph known as a bar chart is used to show and compare the quantity, frequency, or other measure of various discrete data categories. A descriptive statistic is a summary statistic that quantitatively explains or summarizes features from a collection of information. Step 2 A plot of a box and whisker is a way of summing up a set of data collected at aninterval. The graph is used to display the distribution structure, its central meaning and its variability. A flowchart is a diagram which describe an algorithm of a procedure, device or machine. Thus, the most powerful and helpful in determining whether the baseline characteristics of a study group are well balanced is descriptive statistic. Therefore, option B) is correct. Question 3 Determine whether the data described below is quantitative of qualitative variable. A. The data are quantitative because they dont Answer Step 1 It is given that the height of subjects in an experiment when testing a chemical. Step 2 Qualitative data: Qualitative data is defined as the data that categorize or classify the individuals. The values of the qualitative data do not occur naturally on a numerical scale and mathematical operations cannot be performed on these values. That is, the qualitative data are non-numerical measures such as characteristics, attributes, or labels, whereas the quantitative data are numerical measures on which the arithmetic operations are possible. Quantitative data: The variable that consists of numerical quantities that can be counted is termed as quantitative variable. In this case, the correct option is B. The data are quantitative because they consist of counts or measurements. Question 4 What is the difference between quantitative and qualitative data. Answer Step 1 Data are characteristics or information, usually numerical, that are collected through observation. Data is measured, collected and reported, and analyzed, whereupon it can be visualized using graphs, images or other analysis tools. Data is a collection of facts, such as numbers, words, measurements, observations or just descriptions of things. Step 2 Quantitative data -Quantitative data describes quantities or numbers, this data is in the form of numbers that can be examined through various tests, formulas, statistical software, and can be compared on a numeric scale. -Quantitative data is objective, to-the-point, and conclusive. -Quantitative data is considered as structured data. This type of data is formatted in a way so it can be quickly organized and searchable within relational databases. -For example: height of an individual, weight of an individual, length of the tree stem, number of teeth, amount of enzyme produced by an organ, number of eggs laid by a hen, etc. Qualitative data -Qualitative data describes qualities or characteristics and may be in the form of descriptive words that can be examined by patterns, frequency or meaning. -Qualitative data is subjective, interpretive, and exploratory. -Qualitative data is considered unstructured or semi structured. This type of data is loosely formatted with very little structure. Because of this, qualitative data cannot be collected and analyzed using conventional methods. -For example: color of eye, skin color, hair color, weather condition, mood of an individual, taste of food, etc. Question 5 Do the following summarize a categorical variable or a numerical variable? Explain. (1) For a football player, the average number of yards per carry in one game (2) For a basketball player, the shooting percentage during one game (3) For a baseball player, his batting average during the playoffs (4) For a hockey player, the time on ice per game Answer Categorical / qualitative variables places the individuals into a category, while quantitative variable is a numerical variable. (1) The average number of yards are represented by integers or decimal numbers, thus the variable is numerical. (2) The shooting percentage is represented by an integer or decimal number, thus the variable is numerical. (3) The batting averageis represented by an integer or decimal number, thus the variable is numerical. (4) The time on the ice is represented by an integer or decimal number, thus the variable is numerical.