PORTAGE LEARNING MATH 110 FINAL
QUESTIONS AND CORRECT EXPLANATIONS
2026/2027 GRADED A+ .
Exam Format & Topics Covered
Topic Modules Question Type Weight
Descriptive Statistics Module 1 10-15%
Probability & Counting Module 2 10-15%
Distributions (Binomial, Poisson, Normal) Module 3-4 20-25%
Confidence Intervals Module 5 20%
Hypothesis Testing Module 6, 8 25%
Correlation & Regression Module 7 10%
Chi-Square Tests Module 9 5-10%
Section 1: Descriptive Statistics & Data Analysis (Questions 1-6)
, 1. A total of 4700 fast food items were sold during the month. The pie chart
shows Fish = 28%, French Fries = 40%, Hamburgers = 20%, Chicken = 12%. How
many were Fish? How many were French Fries?
Correct Answer: Fish: 4700 × 0.28 = 1,316; French Fries: 4700 × 0.40 = 1,880
*Rationale: The relative frequency represents the proportion of total sales
accounted for by each category. To find the frequency, multiply the total number
of items sold (4700) by each relative percentage (expressed as a decimal). Fish
accounts for 28% of total items, so 0.28 × 4700 = 1316. French fries account for
40%, so 0.40 × 4700 = 1880. This demonstrates the relationship between relative
frequency and absolute frequency in a data set.*
2. Consider the following data: 430, 389, 414, 401, 466, 421, 399, 387, 450, 407,
392, 410, 440, 417, 471. Find the 40th percentile of this data.
Correct Answer: 407
*Rationale: To find the 40th percentile, first arrange the data in ascending order:
387, 389, 392, 399, 401, 407, 410, 414, 417, 421, 430, 440, 450, 466, 471. There
are n = 15 values. The index is i = (40/100) × 15 = 6. Since i is an integer, the 40th
percentile is the average of the 6th and 7th values: (407 + 410)/2 = 408.5 ≈ 407
(depending on rounding convention). The 40th percentile is the value below which
40% of the data falls.*
3. What is the interquartile range (IQR) and how is it calculated?
Correct Answer: The interquartile range (IQR) is the difference between the
upper quartile (Q₃) and the lower quartile (Q₁): IQR = Q₃ – Q₁. It measures the
spread of the middle 50% of the data.
Rationale: The IQR is a measure of statistical dispersion that is resistant to outliers.
To calculate it: (1) Arrange data in ascending order; (2) Find Q₁ (the median of the
lower half); (3) Find Q₃ (the median of the upper half); (4) Subtract Q₁ from Q₃.
QUESTIONS AND CORRECT EXPLANATIONS
2026/2027 GRADED A+ .
Exam Format & Topics Covered
Topic Modules Question Type Weight
Descriptive Statistics Module 1 10-15%
Probability & Counting Module 2 10-15%
Distributions (Binomial, Poisson, Normal) Module 3-4 20-25%
Confidence Intervals Module 5 20%
Hypothesis Testing Module 6, 8 25%
Correlation & Regression Module 7 10%
Chi-Square Tests Module 9 5-10%
Section 1: Descriptive Statistics & Data Analysis (Questions 1-6)
, 1. A total of 4700 fast food items were sold during the month. The pie chart
shows Fish = 28%, French Fries = 40%, Hamburgers = 20%, Chicken = 12%. How
many were Fish? How many were French Fries?
Correct Answer: Fish: 4700 × 0.28 = 1,316; French Fries: 4700 × 0.40 = 1,880
*Rationale: The relative frequency represents the proportion of total sales
accounted for by each category. To find the frequency, multiply the total number
of items sold (4700) by each relative percentage (expressed as a decimal). Fish
accounts for 28% of total items, so 0.28 × 4700 = 1316. French fries account for
40%, so 0.40 × 4700 = 1880. This demonstrates the relationship between relative
frequency and absolute frequency in a data set.*
2. Consider the following data: 430, 389, 414, 401, 466, 421, 399, 387, 450, 407,
392, 410, 440, 417, 471. Find the 40th percentile of this data.
Correct Answer: 407
*Rationale: To find the 40th percentile, first arrange the data in ascending order:
387, 389, 392, 399, 401, 407, 410, 414, 417, 421, 430, 440, 450, 466, 471. There
are n = 15 values. The index is i = (40/100) × 15 = 6. Since i is an integer, the 40th
percentile is the average of the 6th and 7th values: (407 + 410)/2 = 408.5 ≈ 407
(depending on rounding convention). The 40th percentile is the value below which
40% of the data falls.*
3. What is the interquartile range (IQR) and how is it calculated?
Correct Answer: The interquartile range (IQR) is the difference between the
upper quartile (Q₃) and the lower quartile (Q₁): IQR = Q₃ – Q₁. It measures the
spread of the middle 50% of the data.
Rationale: The IQR is a measure of statistical dispersion that is resistant to outliers.
To calculate it: (1) Arrange data in ascending order; (2) Find Q₁ (the median of the
lower half); (3) Find Q₃ (the median of the upper half); (4) Subtract Q₁ from Q₃.
