Unit 14 · Class 8 IB MYP · MCQ Test
Box Plots & Cumulative Frequency MCQ Test — Class 8 IB MYP
Practice 10 multiple-choice questions with instant answer reveal and explanations.
Box Plots & Cumulative Frequency — MCQ Questions
1In a box plot, what does the line inside the box represent?
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Answer: Median
Hint: The box plot shows the five-number summary, and the line inside the box is one of them.
Solution:
The line inside the box represents the median (Q2).
2In a box plot, the 'whiskers' extend to which values?
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Answer: Minimum and maximum
Hint: In a simple box plot (without outlier detection), whiskers go to the extremes.
Solution:
In a basic box plot, whiskers extend from minimum to Q1 and from Q3 to maximum.
3A cumulative frequency table shows that 30 out of 50 students scored 60 or below. What fraction of students scored above 60?
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Answer: \(\frac{2}{5}\)
Hint: Above 60: 50 − 30 = 20. Fraction = 20/50.
Solution:
Students above 60 = 50 − 30 = 20
Fraction = 20/50 = 2/5
4The data set is: 1, 3, 5, 7, 9, 11, 13. What is the five-number summary?
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Answer: 1, 3, 7, 11, 13
Hint: Min = 1, Q1 = median of {1,3,5} = 3, Median = 7, Q3 = median of {9,11,13} = 11, Max = 13.
Solution:
Min = 1, Q1 = 3, Median = 7, Q3 = 11, Max = 13
5What does a cumulative frequency curve (ogive) show?
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Answer: The running total of frequencies up to each value
Hint: Cumulative means 'adding up'.
Solution:
A cumulative frequency curve shows the running total of frequencies.
Each point shows how many data values are less than or equal to that value.
6Which of the following is NOT part of the five-number summary?
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Answer: Mean
Hint: The five-number summary: min, Q1, median, Q3, max.
Solution:
The five-number summary is: minimum, Q1, median, Q3, maximum.
The mean is NOT part of the five-number summary.
7A box plot is symmetric. What can you say about the median?
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Answer: The median is roughly in the centre of the box
Hint: Symmetric means roughly equal spread on both sides of the median.
Solution:
In a symmetric box plot, the median line is roughly in the centre of the box.
This means Q2 − Q1 ≈ Q3 − Q2.
8Two data sets have: Set A (Q1=10, Median=15, Q3=22) and Set B (Q1=12, Median=15, Q3=18). Which has greater spread in the middle 50%?
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Answer: Set A
Hint: Compare IQRs: Set A: 22−10=12, Set B: 18−12=6.
Solution:
Set A IQR = 22 − 10 = 12
Set B IQR = 18 − 12 = 6
Set A has greater spread (larger IQR)
9From the cumulative frequency table: 0-10 (CF=4), 10-20 (CF=14), 20-30 (CF=30), 30-40 (CF=38), 40-50 (CF=40). Estimate the median class.
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Answer: 20-30
Hint: n = 40, so median at CF = 20. The 20th value falls in which class?
Solution:
n/2 = 20
CF goes: 4, 14, 30...
The 20th value is in the 20-30 class (since CF reaches 30 here).
10A box plot shows the median closer to Q3 than Q1. What does this suggest about the distribution?
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Answer: Negatively skewed (left-skewed)
Hint: If the median is closer to Q3, the lower half is more spread out (left tail longer).
Solution:
Median closer to Q3 → left side of box is wider
This means the data is negatively skewed (left-skewed)
The tail extends more to the left.
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Tips for Box Plots & Cumulative Frequency MCQs
- 1Read each question carefully and identify what is being asked before looking at the options.
- 2Try to solve the problem mentally or on paper first, then match your answer with the options.
- 3Use elimination — rule out clearly wrong options to improve your chances even when unsure.
- 4Check units, signs, and edge cases — these are common traps in Box Plots & Cumulative Frequency MCQs.
- 5Review your mistakes after completing the test to build lasting understanding.
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