Example 1easy
A data set has minimum 5, Q1 = 12, median = 18, Q3 = 25, maximum 32. What is the interquartile range (IQR)?
Step-by-step solution
- IQR = Q3 − Q1 = 25 − 12 = 13
Answer: 13
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About Box Plots & Cumulative Frequency — Class 8 IB
Draw box plots, calculate quartiles, and interpret cumulative frequency diagrams. This topic is part of the IB Class 8 mathematics syllabus (chapter: Unit 14). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.
Box Plots & Cumulative Frequency — solved examples for Class 8 IB
Example 2medium
Two 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%?
- A)Set A
- B)Set B
- C)Both the same
- D)Cannot determine
Step-by-step solution
- Set A IQR = 22 − 10 = 12
- Set B IQR = 18 − 12 = 6
- Set A has greater spread (larger IQR)
Answer: Set A
Example 3hard
A dataset of 100 values has CF: 0-20 (CF=8), 20-40 (CF=25), 40-60 (CF=58), 60-80 (CF=85), 80-100 (CF=100). Estimate Q1 using linear interpolation.
Step-by-step solution
- Q1 at CF = 100/4 = 25
- Class 20-40: previous CF = 8, frequency = 17, width = 20
- Q1 = 20 + ((25 − 8)/17) × 20 = 20 + 20 = 40
Answer: 40
Practice questions on Box Plots & Cumulative Frequency
Q1.easy
In a box plot, what does the line inside the box represent?- A)Mean
- B)Median
- C)Mode
- D)Range
Show answer
Answer: Median
Hint: The box plot shows the five-number summary, and the line inside the box is one of them.
Q2.easy
Find the median of: 3, 7, 9, 12, 15, 18, 21.Show answer
Answer: 12
Hint: There are 7 values. The median is the 4th value.
Q3.easy
Find Q1 (lower quartile) of: 2, 5, 7, 8, 12, 14, 16, 20.Show answer
Answer: 6
Hint: Q1 is the median of the lower half: 2, 5, 7, 8.
Q4.medium
A cumulative frequency curve for 60 students shows: at score 50, CF = 15; at score 70, CF = 45. How many students scored between 50 and 70?Show answer
Answer: 30
Hint: Students between 50 and 70 = CF(70) − CF(50).
Q5.medium
From a cumulative frequency curve of 200 data points, Q1 is found at CF = 50, Q3 at CF = 150. If Q1 = 35 and Q3 = 65, find the IQR.Show answer
Answer: 30
Hint: IQR = Q3 − Q1 = 65 − 35.
Q6.medium
A box plot for test scores shows: min=35, Q1=55, median=70, Q3=82, max=98. What percentage of students scored above 82?Show answer
Answer: 25
Hint: Q3 is the 75th percentile. Above Q3 = top 25%.
Q7.hard
A box plot shows: min=2, Q1=15, median=25, Q3=40, max=80. Calculate the upper fence and determine whether max is an outlier.- A)Upper fence = 77.5; max IS an outlier
- B)Upper fence = 77.5; max is NOT an outlier
- C)Upper fence = 62.5; max IS an outlier
- D)Upper fence = 62.5; max is NOT an outlier
Show answer
Answer: Upper fence = 77.5; max IS an outlier
Hint: IQR = 40 − 15 = 25. Upper fence = 40 + 1.5(25) = 77.5. Is 80 > 77.5?
Q8.hard
Two classes have the following box plot data. Class X: min=30, Q1=45, med=55, Q3=65, max=85. Class Y: min=40, Q1=50, med=55, Q3=60, max=70. Which class performed better overall and which was more consistent?- A)Same median; Class Y more consistent (smaller IQR)
- B)Class X better; Class Y more consistent
- C)Class Y better; Class X more consistent
- D)Class X better and more consistent
Show answer
Answer: Same median; Class Y more consistent (smaller IQR)
Hint: Compare medians for 'better'. Compare IQRs for consistency.
Q9.hard
From a CF curve with n=120: Q1=32, median=48, Q3=67. A value of 120 appears in the data. Is it an outlier?- A)Yes
- B)No
Show answer
Answer: Yes
Hint: IQR = 67 − 32 = 35. Upper fence = 67 + 1.5(35) = 119.5.
These are 9 of the 60 questions available for Box Plots & Cumulative Frequency. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.