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Descriptive Statistics Quiz 7 (10 MCQs)

This set of multiple-choice questions evaluates understanding of measurement scales, ratio data, and absolute zero. It tests skills in calculating measures of central tendency, including mean, median, and mode, and the impact of outliers. Concepts such as class interval boundaries, frequency distribution, and descriptive statistics are also covered. Students will interpret numerical data, analyze symmetric distributions, and understand measures of dispersion like standard deviation.

Quiz Instructions

Select an option to see the correct answer instantly.

1. Statistical data are often relevant when discussing psychological disorders. For example, a researcher might want to know how many new cases of depression are diagnosed each year, a figure called the ..... of the disorder.

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

Exam Relevance: AP Psychology, GRE Psychology, MCAT

Difficulty: Easy

Concept notes: Incidence refers to the number of new cases of a disorder diagnosed within a specific time period. It is a measure of the frequency of new cases.

Common Mistakes: A common mistake is confusing incidence with prevalence. Prevalence refers to the total number of cases of a disorder in a population at a given time, not just the new cases.

Explanations: The term "incidence" is used to describe the number of new cases of a disorder diagnosed each year. This is the correct term for the frequency of new cases, which is what the question is asking for.

Option Analysis:

Option A: Prevalence refers to the total number of cases of a disorder in a population at a given time, not just the new cases.
Option B: Incidence refers to the number of new cases of a disorder diagnosed within a specific time period, which is the correct term for the frequency of new cases.
Option C: Recurrence refers to the reappearance of a disorder after a period of remission, not the number of new cases.
Option D: Ratio is a general term for the quantitative relation between two amounts, not specific to the frequency of new cases of a disorder.

2. Observe the frequency distribution:Estimate the class boundaries.

Correct Answer: Correct answer is: (C) 19.5, 30.5, 41.5, 52.5, 63.5, 74.5, 85.5, 96.5.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: Class boundaries are the real limits of the class intervals. They are calculated to ensure that no data point falls on the boundary between two classes.

Common Mistakes: A common mistake is to use the class limits directly as class boundaries without adjusting for the midpoint between classes.

Explanations: Class boundaries are determined by finding the midpoint between the upper limit of one class and the lower limit of the next class. For example, if the class limits are 20-31, 31-42, etc., the class boundaries would be 19.5, 30.5, 41.5, etc. This ensures that each data point falls into one and only one class without ambiguity.

Option Analysis:

Option A: Incorrect because the boundaries are not adjusted to the midpoint between classes.
Option B: Incorrect because it does not include the upper boundary of the last class.
Option C: Correct because it correctly calculates the class boundaries by finding the midpoints between class limits.
Option D: Incorrect because it uses the class limits directly without adjusting for the midpoint.

3. The mean of first five prime numbers is

Correct Answer: Correct answer is: (C) 5.6.

Exam Relevance: SAT, GRE, GMAT, ACT

Difficulty: Moderate

Concept notes: The 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 confuse the mean with other measures of central tendency, such as the median or mode.

Explanations: The first five prime numbers are 2, 3, 5, 7, and 11. To find the mean, we sum these numbers and divide by the count of numbers. \[ \text{Sum} = 2 + 3 + 5 + 7 + 11 = 28 \] \[ \text{Count} = 5 \] \[ \text{Mean} = \frac{28}{5} = 5.6 \]

Option Analysis:

Option A: 5. This is incorrect because the sum of the first five prime numbers divided by 5 is not 5.
Option B: 6. This is incorrect because the sum of the first five prime numbers divided by 5 is not 6.
Option C: 5.6. This is correct because the sum of the first five prime numbers divided by 5 is 5.6.
Option D: 5.8. This is incorrect because the sum of the first five prime numbers divided by 5 is not 5.8.

Mnemonic: Prime Mean: 2, 3, 5, 7, 11, Sum 28, Divide by 5, 5.6

4. Measurements, numbers and percentages

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

Concept notes: Statistics involves the collection, analysis, interpretation, and presentation of data, including measurements, numbers, and percentages.

Common Mistakes: A common mistake is confusing statistics with personal or anecdotal evidence, which relies on individual experiences rather than systematic data collection and analysis.

Explanations: Statistics is the correct answer because it deals with the systematic collection, analysis, and interpretation of data, which includes measurements, numbers, and percentages. Testimonial evidence and personal or anecdotal evidence are not systematic and do not involve the rigorous analysis of data.

Option Analysis:

Option A: Testimonial evidence is based on personal opinions or experiences and does not involve systematic data analysis.
Option B: Statistics involves the systematic collection, analysis, and interpretation of data, including measurements, numbers, and percentages.
Option C: Personal or anecdotal evidence is based on individual experiences and is not systematic or rigorous.
Option D: This option is incorrect as statistics is the correct answer.

5. Can the mean, median and mode of data coincide?

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

Concept notes: In descriptive statistics, the mean, median, and mode can coincide in certain data sets.

Common Mistakes: A common misunderstanding is that the mean, median, and mode are always different. However, in symmetric distributions, particularly in a perfectly symmetrical distribution like a normal distribution, these measures can be the same.

Explanations: In a perfectly symmetrical distribution, such as a normal distribution, the mean, median, and mode are all equal. This is because the mean is the average value, the median is the middle value, and the mode is the most frequent value. In a perfectly symmetrical distribution, these three measures of central tendency will coincide at the center of the distribution.

Option Analysis:

Option A: Correct. The mean, median, and mode can coincide in certain data sets, particularly in symmetric distributions.
Option B: Incorrect. It is possible for the mean, median, and mode to coincide, so this option is not correct.

6. A PIE CHART is done in .....

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

Concept notes: A pie chart is a circular statistical graphic that is divided into slices to illustrate numerical proportion. Each slice's angle is proportional to the quantity it represents, typically expressed as a percentage of the whole.

Common Mistakes: A common misunderstanding is that pie charts use raw frequencies or cumulative frequencies directly. However, pie charts typically represent data as percentages to show the relative proportions of categories.

Explanations: Pie charts are used to show the proportion of each category relative to the whole. Each slice of the pie chart represents a percentage of the total, making it easy to visualize the distribution of data. Therefore, the correct answer is percentages.

Option Analysis:

Option A: Frequencies are not used directly in pie charts; they are converted to percentages.
Option B: Cumulative frequencies are not used in pie charts; they are converted to percentages.
Option C: Percentages are used to represent the proportion of each category in a pie chart.
Option D: Decimals are not the primary representation in pie charts; percentages are used instead.

7. A fact or a piece of data from a study is a what?

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Easy

Concept notes: A statistic is a fact or piece of data obtained from a study of a large quantity of numerical data.

Common Mistakes: A common misunderstanding is that a statistic is only a numerical value, but it can also be a fact derived from data.

Explanations: In descriptive statistics, a statistic is a piece of data or fact derived from a study or analysis of numerical data. This aligns with the definition provided in the question, making "Statistic" the correct answer.

Option Analysis:

Option A: Correct. A statistic is a fact or piece of data from a study.
Option B: Incorrect. A thesis is a statement or theory that is put forward as a premise to be maintained or proved.
Option C: Incorrect. A hook is a literary device used to capture the reader's attention at the beginning of a text.
Option D: Incorrect. This option is not applicable as "Statistic" is the correct answer.

8. For set of data 1, 1, 1, 2, 2, 3, 4, 5, 5, and 25 the mean is 4.9, the median is 2.5, and the mode is 1 Which is the best measure of center to best describes the data set?

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: The median is the middle value in a data set when the values are arranged in ascending or descending order. It is less affected by outliers compared to the mean, which can be skewed by extreme values.

Common Mistakes: A common mistake is to assume that the mean is always the best measure of central tendency. However, in the presence of outliers, the median is often a better choice.

Explanations: The data set provided is 1, 1, 1, 2, 2, 3, 4, 5, 5, 25. The mean is 4.9, which is heavily influenced by the outlier value of 25. The mode is 1, which does not represent the central tendency well due to the presence of other values. The median is 2.5, which is the average of the 5th and 6th values (2 and 3) when the data is ordered. The median is less affected by the outlier and provides a better representation of the central tendency of the data set.

Option Analysis:

Option A: The mean is 4.9, which is heavily influenced by the outlier value of 25 and does not represent the central tendency well.
Option B: The median is 2.5, which is less affected by the outlier and provides a better representation of the central tendency.
Option C: The mode is 1, which is the most frequent value but does not represent the central tendency well due to the presence of other values.
Option D: The range is not a measure of central tendency and is not relevant to this question.

9. Which level of measurement can have absolute zero value?

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

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: The level of measurement that can have an absolute zero value is the ratio level. Absolute zero indicates the absence of the quantity being measured.

Common Mistakes: A common misunderstanding is that interval data can have an absolute zero, but interval data only has a relative zero, not an absolute one.

Explanations: The ratio level of measurement includes a true zero point, which means that zero represents the absence of the quantity being measured. This is a key characteristic of ratio data. For example, temperature in Kelvin has an absolute zero, which means the absence of thermal energy. In contrast, nominal data only categorizes, ordinal data ranks, and interval data measures differences but does not have a true zero point.

Option Analysis:

Option A: Nominal data only categorizes and does not have a numerical value or zero point.
Option B: Ordinal data ranks items but does not have a true zero point or equal intervals.
Option C: Interval data measures differences but does not have a true zero point.
Option D: Ratio data has a true zero point, indicating the absence of the quantity being measured.

Mnemonic: Ratios have Real Zeros.

10. A quantity calculated to indicate the extent of deviation for a group as a whole.

Correct Answer: Correct answer is: (A) Standard deviation.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: Standard deviation is a measure of the dispersion or spread of a dataset. It indicates how much the values in a dataset deviate from the mean.

Common Mistakes: A common misunderstanding is that the mean is a measure of deviation. The mean is actually a measure of central tendency, not dispersion.

Explanations: Standard deviation is the correct answer because it quantifies the extent of deviation for a group as a whole. It measures the average amount by which each data point differs from the mean. This makes it a suitable measure for indicating the spread or variability of a dataset.

Option Analysis:

Option A: Standard deviation is the correct choice as it measures the extent of deviation for a group as a whole.
Option B: The mean is a measure of central tendency, not a measure of deviation.

Frequently Asked Questions

What is descriptive statistics?

Descriptive statistics involves the systematic collection, organization, and summarization of data to provide a clear picture of the data's characteristics.

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 median and how is it determined?

The median is the middle value in a dataset when the values are arranged in order. If there is an even number of values, the median is the average of the two middle values.

What is the mode and when is it useful?

The mode is the value that appears most frequently in a dataset. It is particularly useful for identifying the most common value or category in a set of data.

What is the significance of standard deviation in data analysis?

Standard deviation measures the dispersion or spread of data points around the mean. It helps to understand how much the values in a dataset vary from the average.

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