Q8a. Construct a relative frequency distribution for the survey responses about road construction payment preferences.

Background

Topic: Frequency and Relative Frequency Distributions

This question tests your ability to convert raw frequency counts into relative frequencies (proportions or percentages) for categorical data.

Key Terms and Formulas:

• Frequency: The number of times a response occurs.

• Relative Frequency: The proportion of the total responses for each category.

• Formula:

Step-by-Step Guidance

1. Find the total number of responses by adding the frequencies for all categories.

2. For each response category (New tolls, Increase gas tax, No new roads), divide the frequency by the total number of responses to get the relative frequency.

3. Express the relative frequency as a decimal or percentage for each category.

4. Set up a table with the response categories and their corresponding relative frequencies.

Try solving on your own before revealing the answer!

Q9a. Which was the most popular rating for Hot Doug’s Restaurant?

Background

Topic: Frequency Distribution and Mode

This question tests your ability to interpret a bar graph and identify the mode (most frequent value) in a categorical dataset.

Key Terms:

• Mode: The value that appears most frequently in a dataset.

• Frequency: The number of times each rating was given.

Step-by-Step Guidance

1. Examine the bar graph and note the frequency for each star rating (1 to 5 stars).

2. Identify which bar is the tallest, indicating the highest frequency.

3. The rating corresponding to the tallest bar is the mode, or most popular rating.

Try solving on your own before revealing the answer!

Q10a. Construct a frequency distribution for the serum HDL cholesterol data from 40 patients.

Background

Topic: Frequency Distribution for Quantitative Data

This question tests your ability to organize raw quantitative data into a frequency distribution table, grouping values into classes or intervals.

Key Terms and Formulas:

• Frequency Distribution: A table that shows how many data values fall into each class interval.

• Class Interval: A range of values used to group the data.

• Steps:

Step-by-Step Guidance

1. List all the data values and determine the minimum and maximum values.

2. Decide on the number of classes (intervals) to use for the frequency distribution.

3. Calculate the class width:

4. Set up the class intervals and count how many data values fall into each interval.

Try solving on your own before revealing the answer!

Q11a. Determine the sample mean failure times for each material (A and B).

Background

Topic: Measures of Central Tendency (Mean)

This question tests your ability to calculate the sample mean for two sets of quantitative data.

Key Terms and Formulas:

• Sample Mean (): The average of the sample values.

• Formula:

Step-by-Step Guidance

1. List all the failure times for Material A and Material B.

2. Add up all the values for each material to find the sum.

3. Count the number of values (n) for each material.

4. Divide the sum by the number of values to find the sample mean for each material.

Try solving on your own before revealing the answer!