MAT 133 2-3 HOMEWORK CHAPTER 3 2026/2027 | Complete
Solutions | Pass Guaranteed - A+ Graded
SECTION 1: Measures of Central Tendency (Mean, Median, Mode) (Q1–Q8)
Q1: The ages of 7 students in a study group are: 5, 10, 15, 20, 25, 30, 35. What is the
mean age?
A. 15
B. 18
C. 20 [CORRECT]
D. 25
Correct Answer: C
Rationale: The mean is calculated by summing all values (5+10+15+20+25+30+35 =
140) and dividing by the number of observations (7), yielding 140/7 = 20. Option A is the
median, B is an arbitrary miscalculation, and D is the upper quartile value.
Q2: A real estate agent reports that home prices in a neighborhood are strongly skewed
right due to a few luxury homes. Which measure of central tendency best represents the
typical home price?
A. Mean
B. Median [CORRECT]
C. Mode
D. Weighted mean
Correct Answer: B
Rationale: The median is resistant to extreme values and skewness, making it the
preferred measure for skewed data. The mean is pulled upward by high outliers, the
mode may not exist or be meaningful, and weighted mean is not appropriate here.
Q3: A student's final grade is computed using weighted averages: Exam 1 (weight 20%,
score 75), Exam 2 (weight 30%, score 82), and Final Exam (weight 50%, score 90). What
is the weighted mean?
A. 82.0
B. 84.6 [CORRECT]
, C. 85.3
D. 87.5
Correct Answer: B
Rationale: The weighted mean is 0.20(75) + 0.30(82) + 0.50(90) = 15 + 24.6 + 45 = 84.6.
Option A uses unweighted average, C incorrectly weights the exams equally, and D uses
incorrect weight assignments.
Q4: Which measure of central tendency is most affected by a single extreme outlier?
A. Mean [CORRECT]
B. Median
C. Mode
D. All are equally affected
Correct Answer: A
Rationale: The mean uses every value in its calculation, so extreme outliers directly
influence its value. The median depends only on position and is resistant to outliers,
while the mode depends only on frequency and is also resistant.
Q5: A teacher compares two sections of the same course. Section 1 scores: 70, 75, 80,
85, 90. Section 2 scores: 60, 75, 80, 85, 100. Which statement about measures of center
is true?
A. The mean is higher in Section 2
B. The median is higher in Section 1
C. Both sections have the same mean and median [CORRECT]
D. Neither section has a mode
Correct Answer: C
Rationale: Both sections have mean = 80 and median = 80. The outlier in Section 2 pulls
the mean but is offset symmetrically, while the medians remain identical. Options A and
B are false, and D is irrelevant since neither dataset has a repeating value.
Q6: Two classes took the same exam. Class A has a mean of 72 and a median of 80.
Class B has a mean of 80 and a median of 72. Which statement is most accurate?
A. Class A is skewed right
B. Class B is skewed left
C. The mean is greater than the median in Class A
D. Class B is skewed right [CORRECT]
Correct Answer: D
Solutions | Pass Guaranteed - A+ Graded
SECTION 1: Measures of Central Tendency (Mean, Median, Mode) (Q1–Q8)
Q1: The ages of 7 students in a study group are: 5, 10, 15, 20, 25, 30, 35. What is the
mean age?
A. 15
B. 18
C. 20 [CORRECT]
D. 25
Correct Answer: C
Rationale: The mean is calculated by summing all values (5+10+15+20+25+30+35 =
140) and dividing by the number of observations (7), yielding 140/7 = 20. Option A is the
median, B is an arbitrary miscalculation, and D is the upper quartile value.
Q2: A real estate agent reports that home prices in a neighborhood are strongly skewed
right due to a few luxury homes. Which measure of central tendency best represents the
typical home price?
A. Mean
B. Median [CORRECT]
C. Mode
D. Weighted mean
Correct Answer: B
Rationale: The median is resistant to extreme values and skewness, making it the
preferred measure for skewed data. The mean is pulled upward by high outliers, the
mode may not exist or be meaningful, and weighted mean is not appropriate here.
Q3: A student's final grade is computed using weighted averages: Exam 1 (weight 20%,
score 75), Exam 2 (weight 30%, score 82), and Final Exam (weight 50%, score 90). What
is the weighted mean?
A. 82.0
B. 84.6 [CORRECT]
, C. 85.3
D. 87.5
Correct Answer: B
Rationale: The weighted mean is 0.20(75) + 0.30(82) + 0.50(90) = 15 + 24.6 + 45 = 84.6.
Option A uses unweighted average, C incorrectly weights the exams equally, and D uses
incorrect weight assignments.
Q4: Which measure of central tendency is most affected by a single extreme outlier?
A. Mean [CORRECT]
B. Median
C. Mode
D. All are equally affected
Correct Answer: A
Rationale: The mean uses every value in its calculation, so extreme outliers directly
influence its value. The median depends only on position and is resistant to outliers,
while the mode depends only on frequency and is also resistant.
Q5: A teacher compares two sections of the same course. Section 1 scores: 70, 75, 80,
85, 90. Section 2 scores: 60, 75, 80, 85, 100. Which statement about measures of center
is true?
A. The mean is higher in Section 2
B. The median is higher in Section 1
C. Both sections have the same mean and median [CORRECT]
D. Neither section has a mode
Correct Answer: C
Rationale: Both sections have mean = 80 and median = 80. The outlier in Section 2 pulls
the mean but is offset symmetrically, while the medians remain identical. Options A and
B are false, and D is irrelevant since neither dataset has a repeating value.
Q6: Two classes took the same exam. Class A has a mean of 72 and a median of 80.
Class B has a mean of 80 and a median of 72. Which statement is most accurate?
A. Class A is skewed right
B. Class B is skewed left
C. The mean is greater than the median in Class A
D. Class B is skewed right [CORRECT]
Correct Answer: D
