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Descriptive Statistics Quiz 35 (10 MCQs)

This set of multiple-choice questions evaluates understanding of algebraic manipulation and descriptive statistics, including arithmetic mean, median calculation, frequency distribution, and bivariate data. Concepts such as central tendency, data summarization, and level of measurement are covered, assessing skills in statistical analysis and data categorization.

Quiz Instructions

Select an option to see the correct answer instantly.

1. If the data set is: 5, 7, 9, 11, what is the median?

Correct Answer: Correct answer is: (B) 8.

Exam Relevance: AP Statistics, SAT, GRE, GMAT

Difficulty: Easy

Concept notes: The median is the middle value in a sorted, ascending or descending, 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 mode (most frequent value) or the mean (average value).

Explanations: To find the median of the data set 5, 7, 9, 11, first, we note that the data set is already sorted in ascending order. Since there are 4 numbers (an even number), the median is the average of the two middle numbers. The two middle numbers are 7 and 9. The average of 7 and 9 is (7 + 9) / 2 = 16 / 2 = 8. Therefore, the median is 8.

Option Analysis:

Option A: 11 is incorrect because it is the largest number in the data set, not the median.
Option B: 8 is correct because it is the average of the two middle numbers in the sorted data set.
Option C: 7 is incorrect because it is one of the middle numbers, but not the median for an even number of observations.
Option D: 9 is incorrect because it is one of the middle numbers, but not the median for an even number of observations.

2. The frequency distribution of two variables is known as

Correct Answer: Correct answer is: (A) Bivariate distribution.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

Concept notes: A bivariate distribution describes the frequency distribution of two variables simultaneously.

Common Mistakes: A common misunderstanding is confusing bivariate distribution with multivariate distribution, which involves more than two variables.

Explanations: A bivariate distribution is the correct term for the frequency distribution of two variables. This is because "bi" means two, and "variate" refers to variables. Therefore, a bivariate distribution specifically deals with the joint distribution of two variables.

Option Analysis:

Option A: Correct. Bivariate distribution refers to the frequency distribution of two variables.
Option B: Incorrect. Multivariate distribution involves more than two variables.
Option C: Incorrect. Univariate distribution involves only one variable.
Option D: Incorrect. Sub-multivariate distribution is not a standard term in statistics.

3. The number of times a certain response appears in a data set is known as its .....

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Very Easy

Concept notes: Frequency refers to the number of times a particular value or response appears in a data set.

Common Mistakes: A common misunderstanding is confusing frequency with relative frequency, which is the proportion of times a value appears in the data set.

Explanations: Frequency is the count of how often a specific value or response occurs in a data set. It is a fundamental concept in descriptive statistics used to summarize and describe the distribution of data.

Option Analysis:

Option A: Correct. Frequency is the number of times a response appears in a data set.
Option B: Incorrect. Relative frequency is the proportion of times a response appears, not the count.
Option C: Incorrect. Sigma (σ) is a symbol used to denote the standard deviation, not frequency.
Option D: Incorrect. Theta (θ) is a symbol often used in statistics for parameters, not frequency.

4. Find the average for this data:12, 8, 4, 4

Correct Answer: Correct answer is: (D) 7.

Exam Relevance: SAT, ACT, GRE, GMAT

Difficulty: Easy

Concept notes: The average (mean) of a set of numbers is calculated by summing all the numbers and then dividing by the count of numbers.

Common Mistakes: A common mistake is to add the numbers and forget to divide by the count of numbers.

Explanations: To find the average of the numbers 12, 8, 4, and 4, follow these steps: 1. Sum the numbers: 12 + 8 + 4 + 4 = 28. 2. Count the numbers: There are 4 numbers. 3. Divide the sum by the count: 28 ÷ 4 = 7. Thus, the average is 7.

Option Analysis:

Option A: 24 is incorrect because it is the sum of the numbers, not the average.
Option B: 16 is incorrect because it is not the result of dividing the sum by the count of numbers.
Option C: 9 is incorrect because it is not the result of dividing the sum by the count of numbers.
Option D: 7 is correct because it is the result of dividing the sum of the numbers by the count of numbers.

5. Statistics which is concerned with summarizing values to describe group characteristics of the data.

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

Concept notes: Descriptive statistics involves summarizing and organizing data to describe the characteristics of a dataset. This includes measures such as mean, median, mode, and standard deviation.

Common Mistakes: A common misunderstanding is confusing descriptive statistics with inferential statistics, which involves making inferences about a population based on a sample.

Explanations: Descriptive statistics is concerned with summarizing values to describe the group characteristics of the data. This includes measures such as mean, median, mode, and standard deviation, which provide a clear and concise summary of the dataset.

Option Analysis:

Option A: Correct. Descriptive statistics summarize and describe the characteristics of a dataset.
Option B: Incorrect. Inferential statistics involve making inferences about a population based on a sample.
Option C: Incorrect. Parametric statistics assume certain characteristics about the data distribution, such as normality.
Option D: Incorrect. Non-parametric statistics do not assume a specific distribution of the data.

6. Gender, age-class, religion, type of disease, and blood group are measured on:

Correct Answer: Correct answer is: (A) Nominal scale of measurement.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

Concept notes: The nominal scale of measurement is used for variables that are categorized without any intrinsic order or quantitative value. Examples include gender, age-class, religion, type of disease, and blood group.

Common Mistakes: A common mistake is to confuse the nominal scale with the ordinal scale, which involves categories that have a natural order or ranking.

Explanations: Gender, age-class, religion, type of disease, and blood group are all examples of variables that are categorized into distinct groups without any inherent order or quantitative value. These variables are best described using the nominal scale of measurement, which is used for qualitative data that can be classified into mutually exclusive categories.

Option Analysis:

Option A: Correct. Gender, age-class, religion, type of disease, and blood group are all examples of nominal data.
Option B: Incorrect. The ordinal scale is used for data that can be ranked or ordered, which is not applicable here.
Option C: Incorrect. The interval scale is used for data with equal intervals but no true zero point, which is not applicable here.
Option D: Incorrect. The ratio scale is used for data with equal intervals and a true zero point, which is not applicable here.

7. A statistical measure based upon the entire population is called parameter while measure based upon a sample is known as:[2008-JUNE]

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

Concept notes: In descriptive statistics, a parameter is a numerical value that describes a characteristic of an entire population, while a statistic is a numerical value that describes a characteristic of a sample.

Common Mistakes: A common misunderstanding is confusing the terms "parameter" and "statistic." A parameter is based on the entire population, while a statistic is based on a sample from the population.

Explanations: A statistical measure based on the entire population is called a parameter. A measure based on a sample is called a statistic. Therefore, the correct answer is "Statistics."

Option Analysis:

Option A: "Sample parameter" is not a correct term in statistics. Parameters are associated with populations, not samples.
Option B: "Inference" refers to the process of making conclusions about a population based on sample data, not a measure based on a sample.
Option C: "Statistics" is the correct term for a measure based on a sample.
Option D: "None of these" is incorrect because "Statistics" is the correct answer.

8. Temperature can be classified into this level of measurement.

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

Concept notes: Temperature is classified as an interval level of measurement because it has equal intervals between values but lacks a true zero point.

Common Mistakes: A common misunderstanding is to confuse temperature with ratio level measurement, which has a true zero point (e.g., weight, height).

Explanations: Temperature is measured on an interval scale because the differences between temperatures are consistent and meaningful, but the zero point is arbitrary (e.g., 0°C does not mean the absence of temperature). This is why temperature is classified as interval level measurement.

Option Analysis:

Option A: Correct. Temperature is an interval level of measurement.
Option B: Incorrect. Ratio level measurement has a true zero point, which temperature does not have.
Option C: Incorrect. Nominal level measurement involves categories without any order or quantitative value.
Option D: Incorrect. Ordinal level measurement involves categories with a specific order but without consistent intervals.

9. A GOOD AVERAGE SHOULD BE CAPABLE OF FURTHER ALGEBRAIC TREATMENT.

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: A good average should be capable of further algebraic treatment because it allows for more advanced statistical analysis and manipulation.

Common Mistakes: A common misunderstanding is that an average is just a simple measure of central tendency and does not require further algebraic treatment.

Explanations: A good average, such as the arithmetic mean, is capable of further algebraic treatment. This means that it can be used in various mathematical operations and formulas, such as calculating the variance, standard deviation, or in regression analysis. This capability enhances the utility of the average in descriptive statistics and allows for deeper analysis of data.

Option Analysis:

Option A: This option is correct because a good average should be capable of further algebraic treatment, which is a desirable property in descriptive statistics.
Option B: This option is incorrect because it contradicts the desirable property of a good average being capable of further algebraic treatment.

10. The word Average and Mean are the same

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Very Easy

Concept notes: In descriptive statistics, the terms "average" and "mean" are often used interchangeably to refer to the same concept.

Common Mistakes: A common misunderstanding is that "average" and "mean" are different measures, but in the context of descriptive statistics, they are the same.

Explanations: In descriptive statistics, the term "average" is commonly used to refer to the arithmetic mean, which is the sum of all values divided by the number of values. Therefore, the terms "average" and "mean" are synonymous in this context.

Option Analysis:

Option A: Correct. The terms "average" and "mean" are the same in descriptive statistics.
Option B: Incorrect. The terms "average" and "mean" are not different in descriptive statistics.

Frequently Asked Questions

What is the purpose of descriptive statistics?

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

How is the arithmetic mean calculated?

The arithmetic mean is calculated by summing all the values in a dataset and then dividing by the number of values.

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

A population parameter is a numerical characteristic of an entire population, while a sample statistic is a numerical characteristic of a subset of the population.

How do you calculate the median when there is an even number of observations?

When there is an even number of observations, the median is calculated by finding the average of the two middle values.

What is a bivariate distribution?

A bivariate distribution describes the joint distribution of two variables, showing how they vary together.

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