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Descriptive Statistics Quiz 39 (10 MCQs)

This set of multiple-choice questions evaluates understanding of measuring correlation using Spearman's rank correlation and descriptive statistics, including arithmetic mean, median, mode, and data summarization techniques. It covers concepts such as ordinal data, rank-based statistics, and measures of central tendency.

Quiz Instructions

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1. Your psychology teacher wants you to organize and summarize the scores on the first psychology test; which type of statistics is your professor most likely to use?

Correct Answer: Correct answer is: (A) Descriptive statistics.

Exam Relevance: AP Statistics, GRE Quantitative, SAT Math

Difficulty: Easy

Concept notes: Descriptive statistics are used to organize, summarize, and present data in a meaningful way. They provide a clear and concise summary of the data, making it easier to understand and interpret.

Common Mistakes: A common misunderstanding is that inferential statistics are needed to summarize data, but descriptive statistics are specifically designed for this purpose.

Explanations: Descriptive statistics are the appropriate choice for organizing and summarizing the scores on the first psychology test. Descriptive statistics include measures such as mean, median, mode, range, and standard deviation, which help to provide a clear and concise summary of the test scores. These measures allow the teacher to understand the distribution and central tendency of the scores, making it easier to interpret the performance of the students.

Option Analysis:

Option A: Correct. Descriptive statistics are used to organize and summarize data.
Option B: Incorrect. Inferential statistics are used to make inferences about a population based on a sample, not to summarize data.
Option C: Incorrect. Correlational statistics are used to measure the relationship between two variables, not to summarize data.
Option D: Incorrect. "Significant statistics" is not a recognized term in statistics. The term "statistical significance" is used to determine if a result is likely due to chance or not.

2. What is the median of this data set?3, 17, 17, 11, 8, 13, 5, 18

Correct Answer: Correct answer is: (B) 12.

Exam Relevance: AP Statistics, SAT, GRE, GMAT

Difficulty: Moderate

Concept notes: The median is the middle value in a sorted list of numbers. If the list has an even number of observations, the median is the average of the two middle numbers.

Common Mistakes: A common mistake is to confuse the median with the mean (average) or mode (most frequent value). Another mistake is not sorting the data before finding the median.

Explanations: To find the median, first sort the data set: 3, 5, 8, 11, 13, 17, 17, 18. Since there are 8 numbers (an even count), the median is the average of the 4th and 5th numbers. The 4th number is 11 and the 5th number is 13. The average of 11 and 13 is (11 + 13) / 2 = 12. Therefore, the median is 12.

Option Analysis:

Option A: 11 is incorrect because it is one of the middle values, but not the median for an even number of observations.
Option B: 12 is correct because it is the average of the two middle values in the sorted list.
Option C: 13 is incorrect because it is one of the middle values, but not the median for an even number of observations.
Option D: 17 is incorrect because it is not a middle value in the sorted list.

Mnemonic: Median: Middle, Mean of Middle

3. What is ordinal (rank) data?

Correct Answer: Correct answer is: (A) Quantitative data that can be given an order or ranked.

Exam Relevance: AP Statistics, GRE, GMAT

Difficulty: Easy

Concept notes: Ordinal data, also known as rank data, is a type of quantitative data where the values have a natural, meaningful order, but the differences between the values may not be equal.

Common Mistakes: A common misunderstanding is that ordinal data must be qualitative. However, ordinal data can be quantitative and still maintain a rank order.

Explanations: Ordinal data is quantitative data that can be ranked or ordered. For example, a survey might ask respondents to rate their satisfaction on a scale from 1 to 5, where 1 is "very unsatisfied" and 5 is "very satisfied." The numbers represent a rank order, but the differences between the numbers may not be equal. This makes it distinct from interval or ratio data, where the differences between values are meaningful and consistent.

Option Analysis:

Option A: Correct. Ordinal data is quantitative data that can be given an order or ranked.
Option B: Incorrect. Ordinal data can be quantitative, not always qualitative.
Option C: Incorrect. Ordinal data can be measured, as it involves ranking or ordering.
Option D: Incorrect. Ordinal data is not always continuous; it can be discrete.

4. Using the measures of central tendency is an example of ..... statistics.

Correct Answer: Correct answer is: (D) Descriptive.

Exam Relevance: AP Statistics, IB Mathematics, GRE Quantitative Reasoning

Difficulty: Easy

Concept notes: Descriptive statistics involves summarizing and organizing data to make it more understandable. Measures of central tendency, such as mean, median, and mode, are used to describe the center of a dataset.

Common Mistakes: A common misunderstanding is confusing descriptive statistics with inferential statistics. Descriptive statistics describe the data at hand, while inferential statistics make inferences about a larger population based on a sample.

Explanations: Measures of central tendency, such as mean, median, and mode, are used to summarize and describe the central point of a dataset. These measures fall under the category of descriptive statistics because they provide a concise summary of the data without making inferences about a larger population.

Option Analysis:

Option A: Instinctual is not a statistical term and does not relate to summarizing data.
Option B: Experimental statistics involve designing and analyzing experiments, not summarizing data.
Option C: Inferential statistics involve making inferences about a population based on a sample, not summarizing the data itself.
Option D: Descriptive statistics involve summarizing and describing the data, which aligns with the use of measures of central tendency.

5. What type of evidence is this: About 37% of 12th graders reported vaping in 2018, compared with 28% in 2017.

Correct Answer: Correct answer is: (A) Statistics.

Exam Relevance: AP Statistics, GRE, SAT

Difficulty: Easy

Concept notes: Statistics involve the collection, analysis, interpretation, and presentation of data. In this context, the given information is a statistical measure showing the percentage of 12th graders who reported vaping in two different years.

Common Mistakes: A common misunderstanding might be confusing statistics with raw data. While the data itself is factual, the presentation of percentages over time is a statistical measure.

Explanations: The statement provides percentages of 12th graders who reported vaping in 2018 and 2017. This type of information is a statistical measure, as it involves the analysis and presentation of data over time. Statistics are used to summarize and interpret data, which is exactly what this statement does.

Option Analysis:

Option A: Correct. The statement provides statistical data on vaping among 12th graders over two years.
Option B: Incorrect. Data refers to the raw information collected, not the analysis or presentation of that information.
Option C: Incorrect. A fact is a statement that can be proven true or false, but it does not necessarily involve statistical analysis.
Option D: Incorrect. A research study typically involves a more comprehensive investigation and analysis, not just a single statistical measure.

6. A data set can have more than one .....

Correct Answer: Correct answer is: (B) Mode.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: In descriptive statistics, a data set can have more than one mode. The mode is the value that appears most frequently in a data set. If multiple values appear with the same highest frequency, the data set is considered multimodal.

Common Mistakes: A common misunderstanding is that a data set can only have one mode. However, a data set can have multiple modes if more than one value appears with the highest frequency.

Explanations: The mode is the value that appears most frequently in a data set. If multiple values appear with the same highest frequency, the data set is considered multimodal. Therefore, a data set can have more than one mode. The median, mean, and midrange are unique values and cannot have multiple instances in a single data set.

Option Analysis:

Option A: The median is the middle value in a data set when the values are arranged in order. A data set cannot have more than one median.
Option B: The mode is the value that appears most frequently in a data set. A data set can have more than one mode if multiple values appear with the same highest frequency.
Option C: The mean is the average value of a data set. A data set cannot have more than one mean.
Option D: The midrange is the average of the maximum and minimum values in a data set. A data set cannot have more than one midrange.

7. Calculate the mean:81, 69, 72, 80, 67, 62, 78, 74, 71, 86

Correct Answer: Correct answer is: (D) 74.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: The mean is calculated by summing all the values and dividing by the number of values.

Common Mistakes: A common mistake is to confuse the mean with the median or mode, or to miscalculate the sum or the number of values.

Explanations: To calculate the mean, sum all the values: 81 + 69 + 72 + 80 + 67 + 62 + 78 + 74 + 71 + 86 = 740. Then, divide the sum by the number of values, which is 10. Therefore, the mean is 740 / 10 = 74.

Option Analysis:

Option A: 82.2 is incorrect because the sum of the values divided by 10 does not equal 82.2.
Option B: 92 is incorrect because the sum of the values divided by 10 does not equal 92.
Option C: 67.2 is incorrect because the sum of the values divided by 10 does not equal 67.2.
Option D: 74 is correct because the sum of the values divided by 10 equals 74.

8. Which one of the following methods serve to measure correlation between two variables?

Correct Answer: Correct answer is: (D) Coefficient of Rank Correlation.

Exam Relevance: AP Statistics, GRE, GMAT, SAT, ACT

Difficulty: Moderate

Concept notes: The Coefficient of Rank Correlation is a statistical measure that assesses the strength and direction of the relationship between two ranked variables. It is particularly useful when the data is not normally distributed or when the variables are ordinal.

Common Mistakes: A common misunderstanding is that a scatter diagram or a two-way table can directly measure correlation. While these tools can visually represent the relationship between two variables, they do not provide a numerical measure of correlation.

Explanations: The Coefficient of Rank Correlation, such as Spearman's rank correlation coefficient, quantifies the degree of association between two ranked variables. It ranges from -1 to +1, where -1 indicates a perfect negative correlation, +1 indicates a perfect positive correlation, and 0 indicates no correlation. This method is particularly useful in descriptive statistics for understanding the relationship between two ordinal or ranked variables.

Option Analysis:

Option A: A two-way table is used to display the frequency distribution of two categorical variables but does not measure correlation.
Option B: A scatter diagram visually represents the relationship between two variables but does not provide a numerical measure of correlation.
Option C: A frequency distribution shows the frequency of occurrence of different values in a dataset but does not measure the relationship between two variables.
Option D: The Coefficient of Rank Correlation measures the strength and direction of the relationship between two ranked variables, making it the correct choice.

Mnemonic: Rank Correlation: "Ranks Correlated, Coefficient Measures"

9. The statistic is a number describing the:

Correct Answer: Correct answer is: (B) Sample.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

Concept notes: In descriptive statistics, a statistic is a numerical value that summarizes a characteristic of a sample.

Common Mistakes: A common misunderstanding is that a statistic describes the entire population, but it actually describes a sample from the population.

Explanations: A statistic is a number that describes a characteristic of a sample. In descriptive statistics, we use statistics to summarize and describe the data from a sample. This is in contrast to a parameter, which describes a characteristic of the entire population.

Option Analysis:

Option A: A population is the entire group of interest, not a number describing it.
Option B: A sample is a subset of the population, and a statistic describes a characteristic of this subset.
Option C: A survey is a method of collecting data, not a number describing it.
Option D: A percent is a type of statistic, but the question asks for the broader category that a statistic describes.

10. Which of the following is an example of a statistic?

Correct Answer: Correct answer is: (B) The average test score was 76.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

Concept notes: A statistic is a numerical value that summarizes a characteristic of a sample or dataset. In this context, the average test score is a statistic because it summarizes the performance of a group of students.

Common Mistakes: A common misunderstanding is to confuse a statistic with a parameter, which describes a characteristic of a population, or with a non-numerical statement.

Explanations: The average test score of 76 is a numerical summary of a sample of test scores, making it a statistic. The other options do not represent numerical summaries of data.

Option Analysis:

Option A: This is a mathematical expression and not a statistic.
Option B: This is a statistic because it is a numerical summary of a sample of test scores.
Option C: This is a statement about a future event and not a statistic.
Option D: This is a prediction and not a numerical summary of data.

Frequently Asked Questions

What is the purpose of descriptive statistics?

Descriptive statistics summarize and organize data to make it more understandable. They provide a clear overview of the main features of a dataset.

How is the median calculated for an even number of observations?

For an even number of observations, the median is calculated by finding the average of the two middle values. This provides a central value that represents the dataset.

What is the coefficient of rank correlation?

The coefficient of rank correlation, such as Spearman's rank correlation, measures the strength and direction of the relationship between two ranked variables. It ranges from -1 to 1.

What is the difference between a population parameter and a sample statistic?

A population parameter is a numerical summary of the entire population, while a sample statistic is a numerical summary of a subset of the population, used to estimate the parameter.

How can descriptive statistics be applied in real-world scenarios?

Descriptive statistics can be used to analyze trends, such as vaping trends, or to summarize test scores. They help in making informed decisions based on data summaries.

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