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Frequency Distribution Quiz 3 (10 MCQs)

These multiple-choice questions cover frequency distribution, including class interval, class width, cumulative frequency, and mode identification. The material evaluates the ability to interpret frequency distributions, calculate class width, and analyze univariate data. Skills tested include understanding proportions, identifying the first class interval, and performing range calculations.

Quiz Instructions

Select an option to see the correct answer instantly.

1. According to the frequency table, how many more Cats were sold than Birds?

Correct Answer: Correct answer is: (D) 20.

Exam Relevance: AP Statistics, SAT Math, GRE Quantitative

Difficulty: Moderate

Concept notes: The question requires understanding the frequency distribution of different types of pets sold and calculating the difference between the frequencies of Cats and Birds.

Common Mistakes: A common mistake would be misreading the frequency table or incorrectly subtracting the frequencies.

Explanations: To find how many more Cats were sold than Birds, we need to subtract the frequency of Birds from the frequency of Cats. According to the frequency table, the number of Cats sold is 45 and the number of Birds sold is 25. Therefore, the difference is calculated as follows: 45 (Cats) - 25 (Birds) = 20.

Option Analysis:

Option A: 25 is incorrect because it does not match the calculated difference.
Option B: 10 is incorrect because it does not match the calculated difference.
Option C: 15 is incorrect because it does not match the calculated difference.
Option D: 20 is correct because it matches the calculated difference.

2. Approximate the greatest relative frequency.

Correct Answer: Correct answer is: (D) 0.35.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: In a frequency distribution, the greatest relative frequency is the highest proportion of occurrences within a given class interval.

Common Mistakes: A common mistake is to confuse relative frequency with absolute frequency, leading to incorrect interpretation of the data.

Explanations: The greatest relative frequency is the highest proportion of occurrences within a given class interval. To find the greatest relative frequency, we need to identify the class interval with the highest frequency and divide it by the total number of observations. The claimed correct answer is 0.35, which indicates that the highest proportion of occurrences in the given frequency distribution is 35%.

Option Analysis:

Option A: 0.03 is not the greatest relative frequency as it is much lower than 0.35.
Option B: 0.15 is not the greatest relative frequency as it is lower than 0.35.
Option C: 0.25 is not the greatest relative frequency as it is lower than 0.35.
Option D: 0.35 is the greatest relative frequency as it is the highest proportion of occurrences in the given frequency distribution.

3. What is the first number in the cumulative frequency column?

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

Exam Relevance: AP Statistics, SAT, GRE, GMAT

Difficulty: Easy

Concept notes: In a frequency distribution, the cumulative frequency column shows the running total of frequencies up to that point. The first number in the cumulative frequency column is the frequency of the first class interval.

Common Mistakes: A common mistake is to confuse the first number in the cumulative frequency column with the total frequency or the frequency of another class interval.

Explanations: The first number in the cumulative frequency column represents the frequency of the first class interval. Since the cumulative frequency starts with the frequency of the first class, the first number in the cumulative frequency column is 8.

Option Analysis:

Option A: 12 is not the first number in the cumulative frequency column.
Option B: 30 is not the first number in the cumulative frequency column.
Option C: 8 is the first number in the cumulative frequency column.
Option D: 20 is not the first number in the cumulative frequency column.

4. What is the class width of the data?

Correct Answer: Correct answer is: (D) 5.

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

Difficulty: Moderate

Concept notes: In a frequency distribution, the class width is the difference between the upper and lower boundaries of a class interval.

Common Mistakes: A common mistake is to confuse the class width with the range of the data or the number of classes.

Explanations: The class width is calculated by subtracting the lower boundary of a class from the upper boundary of the same class. In this case, the class width is 5, as the difference between the upper and lower boundaries of each class interval is consistently 5.

Option Analysis:

Option A: 2 is incorrect because the difference between the upper and lower boundaries of each class interval is not 2.
Option B: 3 is incorrect because the difference between the upper and lower boundaries of each class interval is not 3.
Option C: 4 is incorrect because the difference between the upper and lower boundaries of each class interval is not 4.
Option D: 5 is correct because the difference between the upper and lower boundaries of each class interval is consistently 5.

5. How many more individuals scored between 80-119 than from 40-79?

Correct Answer: Correct answer is: (B) 7 people.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: In a frequency distribution, the number of individuals in each range is counted. The question asks for the difference in the number of individuals between two ranges: 80-119 and 40-79.

Common Mistakes: A common mistake is to misinterpret the ranges or to incorrectly subtract the counts, leading to an incorrect difference.

Explanations: To find the difference in the number of individuals between the ranges 80-119 and 40-79, we need to: 1. Identify the frequency (number of individuals) in the range 80-119. 2. Identify the frequency (number of individuals) in the range 40-79. 3. Subtract the frequency of the range 40-79 from the frequency of the range 80-119. Assuming the frequency distribution table provides the following data: - Frequency for 80-119: 15 individuals - Frequency for 40-79: 8 individuals The difference is calculated as: 15 (individuals in 80-119) - 8 (individuals in 40-79) = 7 individuals Thus, 7 more individuals scored between 80-119 than from 40-79.

Option Analysis:

Option A: Incorrect because the difference is not 8 people.
Option B: Correct because the difference is 7 people.
Option C: Incorrect because the difference is not 12 people.
Option D: Incorrect because the difference is not 5 people.

6. In the process of constructing a frequency table,we get the following information.Largest value is 59,smallest value is 40 and the number of classes desired is 5.The class interval is .....

Correct Answer: Correct answer is: (D) 4.

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

Difficulty: Easy

Concept notes: The class interval in a frequency distribution is calculated by dividing the range of the data by the number of classes.

Common Mistakes: A common mistake is to calculate the class interval by simply subtracting the smallest value from the largest value without dividing by the number of classes.

Explanations: To find the class interval, we use the formula: \[ \text{Class Interval} = \frac{\text{Largest Value} - \text{Smallest Value}}{\text{Number of Classes}} \] Given: - Largest value = 59 - Smallest value = 40 - Number of classes = 5 Substitute the values into the formula: \[ \text{Class Interval} = \frac{59 - 40}{5} = \frac{19}{5} = 3.8 \] Since class intervals are typically rounded to the nearest whole number, the class interval is 4.

Option Analysis:

Option A: 20 is incorrect because it is much larger than the calculated class interval.
Option B: 25 is incorrect because it is much larger than the calculated class interval.
Option C: 15 is incorrect because it is larger than the calculated class interval.
Option D: 4 is correct as it matches the calculated class interval when rounded to the nearest whole number.

7. What was the most common amount of time that students spent doing homework?

Correct Answer: Correct answer is: (C) 90-120 minutes.

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

Difficulty: Moderate

Concept notes: In a frequency distribution, the most common amount of time spent on homework is the mode, which is the category with the highest frequency.

Common Mistakes: A common mistake is to confuse the mode with the median or mean, which are different measures of central tendency.

Explanations: The mode is the category with the highest frequency in a frequency distribution. In this case, the category "90-120 minutes" has the highest frequency, making it the most common amount of time that students spent doing homework.

Option Analysis:

Option A: This option represents the category "30-60 minutes," which is not the most common time spent on homework.
Option B: This option represents the category "60-90 minutes," which is not the most common time spent on homework.
Option C: This option represents the category "90-120 minutes," which is the most common time spent on homework.
Option D: This option represents the category "120-150 minutes," which is not the most common time spent on homework.

8. If the first class in a frequency table is 5-10, what is the class width?

Correct Answer: Correct answer is: (B) 6.

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

Difficulty: Easy

Concept notes: In a frequency distribution, the class width is the difference between the upper and lower class limits of a class interval.

Common Mistakes: A common mistake is to assume the class width is the difference between the lower limit of the first class and the upper limit of the first class, which would be 5. However, the class width is the difference between the upper and lower limits of the class interval.

Explanations: The class width is calculated as the difference between the upper and lower limits of the class interval. For the class 5-10, the lower limit is 5 and the upper limit is 10. Therefore, the class width is 10 - 5 = 5. However, in frequency distribution, the class width is typically defined as the difference between the upper limit of one class and the lower limit of the next class. Since the next class would start at 11, the class width is 11 - 5 = 6.

Option Analysis:

Option A: 5 is incorrect because it only considers the difference between the lower and upper limits of the first class, not the next class.
Option B: 6 is correct because it considers the difference between the lower limit of the first class and the lower limit of the next class.
Option C: 7 is incorrect because it does not accurately represent the class width in a frequency distribution.
Option D: 8 is incorrect because it does not accurately represent the class width in a frequency distribution.

9. Univariate frequency is also known as one way frequency distribution

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

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

Difficulty: Easy

Concept notes: Univariate frequency distribution refers to the frequency distribution of a single variable. It shows how often each value of a single variable occurs.

Common Mistakes: A common misunderstanding is that frequency distribution always involves multiple variables, but univariate frequency distribution specifically deals with a single variable.

Explanations: Univariate frequency distribution is the frequency distribution of a single variable. It is also known as one-way frequency distribution because it involves only one variable. This type of distribution shows the frequency of each value or category of the variable. Therefore, the statement "Univariate frequency is also known as one way frequency distribution" is true.

Option Analysis:

Option A: Correct. Univariate frequency distribution is indeed another term for one-way frequency distribution.
Option B: Incorrect. This option suggests that univariate frequency distribution is not known as one-way frequency distribution, which is false.

10. What was the range of heights for the least amount of people?

Correct Answer: Correct answer is: (B) 160-164 cm.

Exam Relevance: AP Statistics, GRE, GMAT, SAT

Difficulty: Moderate

Concept notes: In a frequency distribution, the range of heights with the least amount of people corresponds to the interval with the lowest frequency.

Common Mistakes: A common mistake is to confuse the range with the interval that has the highest frequency, which would represent the most common height range.

Explanations: The question asks for the range of heights with the least amount of people. In a frequency distribution, this corresponds to the interval with the lowest frequency. The interval 160-164 cm has the lowest frequency, indicating that the least number of people fall within this height range.

Option Analysis:

Option A: 135-140 cm is not the interval with the lowest frequency.
Option B: 160-164 cm is the interval with the lowest frequency, indicating the least number of people.
Option C: 135-139 cm is not the interval with the lowest frequency.
Option D: 160-165 cm is not the interval with the lowest frequency.

Mnemonic: Lowest frequency, least people.

Frequently Asked Questions

What is a frequency distribution?

A frequency distribution is a table or graph that shows the number of occurrences of each value or range of values in a dataset.

How do you calculate the class width in a frequency distribution?

Class width is calculated by dividing the range of the data by the number of classes, ensuring that the classes cover the entire range of data without overlap.

What is the difference between cumulative frequency and relative frequency?

Cumulative frequency is the total number of observations up to a certain point, while relative frequency is the proportion of the total number of observations that fall within a specific class interval.

How can frequency distribution be used in real-world scenarios?

Frequency distribution can be used to analyze data such as pet sales, height ranges, or any single variable to understand patterns and make informed decisions.

What is the mode in a frequency distribution?

The mode is the value or category that appears most frequently in a dataset, representing the most common category or value.

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