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Statistics (Measures of Spread) — Class 9 IB (2025-26)

About Statistics (Measures of Spread) — Class 9 IB

Calculate range, interquartile range, and interpret box plots and cumulative frequency diagrams. This topic is part of the IB Class 9 mathematics syllabus (chapter: Unit 8). On this page you can practice 59 questions across three difficulty levels — 20 easy, 20 medium, and 19 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.

Statistics (Measures of Spread) — solved examples for Class 9 IB

Example 1easy

Which of the following statements best explains why the Interquartile Range (IQR) is often considered a more reliable measure of spread than the Range?

A)The IQR is less affected by extreme values or outliers compared to the Range.
B)The IQR is always a larger value than the Range, making it more comprehensive.
C)The IQR includes all data points in its calculation, unlike the Range.
D)The IQR is simpler to calculate than the Range.

Step-by-step solution

The Range is calculated as the difference between the maximum and minimum values in a data set.
The Interquartile Range (IQR) is the difference between the upper quartile (Q3) and the lower quartile (Q1).
Because the Range depends only on the two most extreme values, it is highly sensitive to outliers. The IQR, however, focuses on the middle 50% of the data, making it robust to extreme values and thus a more reliable measure of spread in the presence of outliers.

Answer: The IQR is less affected by extreme values or outliers compared to the Range.

Example 2medium

The heights (in cm) of 11 students in a class are given below: 150, 162, 155, 170, 168, 152, 160, 175, 158, 165, 172. What is the range of their heights?

A)15 cm
B)20 cm
C)25 cm
D)30 cm

Step-by-step solution

First, order the data set from smallest to largest: 150, 152, 155, 158, 160, 162, 165, 168, 170, 172, 175.
Identify the maximum value (highest height): Maximum = 175 cm.
Identify the minimum value (lowest height): Minimum = 150 cm.
Calculate the range: Range = Maximum Value - Minimum Value.
$Range = 175 cm - 150 cm = 25 cm.$

Answer: 25 cm

Example 3hard

A dataset consists of the numbers: `12, 18, 25, 30, x, 42, 50`. The interquartile range (IQR) is known to be 24. What is the smallest possible integer value for x?

A)A) 15
B)B) 18
C)C) 20
D)D) 25

Step-by-step solution

For a dataset with n=7 data points, when arranged in ascending order, Q1 is the 2nd value and Q3 is the 6th value. Let the sorted dataset be y1, y2, y3, y4, y5, y6, y7.
The given numbers are 12, 18, 25, 30, 42, 50. If x is placed such that it doesn't become y2 or y6, then y2=18 and y6=42. In this case, IQR = Q3 - Q1 = 42 - 18 = 24. This matches the given IQR.
For y2 to remain 18, x must be greater than or equal to 18 (i.e., x ≥ 18), so that 18 is still the second smallest value. For y6 to remain 42, x must be less than or equal to 42 (i.e., x ≤ 42), so that 42 is still the sixth smallest value.
Combining these conditions, x must be an integer in the range [18, 42]. The smallest possible integer value for x that satisfies these conditions is 18.

Answer: B) 18

Practice questions on Statistics (Measures of Spread)

Q1.easy
A group of students recorded their scores on a recent math quiz: 12, 18, 15, 20, 10, 17, 13. What is the range of these scores?
1. A)7
2. B)10
3. C)12
4. D)20
Show answer
Answer: 10
Hint: Remember that the range measures the total spread from the lowest to the highest value in a data set.
Q2.easy
Ravi was asked to find the lower quartile (Q1) of the following ordered data set: 5, 8, 10, 12, 15, 18, 20, 22. He stated that Q1 is 12. Which statement describes the likely mistake Ravi made?
1. A)He confused Q1 with the upper quartile (Q3).
2. B)He mistakenly identified the median of the entire data set as Q1.
3. C)He simply picked the 4th value from the ordered data set.
4. D)He calculated the range instead of Q1.
Show answer
Answer: He simply picked the 4th value from the ordered data set.
Hint: When finding quartiles, you need to find the median of the specific half of your data, not just pick a value based on its position in the full set.
Q3.easy
Two brands of batteries, A and B, were tested for their lifespan in hours. Brand A had a range of 25 hours and an IQR of 10 hours. Brand B had a range of 30 hours and an IQR of 8 hours. Which statement provides the best interpretation of these results?
1. A)Brand A batteries generally last longer than Brand B batteries.
2. B)Brand B batteries are more consistent in their lifespan than Brand A batteries.
3. C)Brand A batteries have more extreme variations in lifespan compared to Brand B.
4. D)Both brands have similar consistency, as their ranges and IQRs are quite close.
Show answer
Answer: Brand B batteries are more consistent in their lifespan than Brand A batteries.
Hint: Remember that a smaller measure of spread, especially the IQR, indicates greater consistency in the central data.
Q4.medium
For the data set: 23, 18, 20, 25, 22, 21, 24, 26, 19, find the interquartile range (IQR).
1. A)5
2. B)6
3. C)7
4. D)8
Show answer
Answer: 5
Hint: Remember to order the data first, then find the median (Q2), followed by Q1 (median of the lower half) and Q3 (median of the upper half).
Q5.medium
Which statement best describes the effect of an outlier on measures of spread?
1. A)Outliers always increase both the range and the interquartile range (IQR).
2. B)Outliers have a significant effect on the range but a minimal effect on the interquartile range (IQR).
3. C)Outliers have a minimal effect on the range but a significant effect on the interquartile range (IQR).
4. D)Outliers decrease the range and increase the interquartile range (IQR).
Show answer
Answer: Outliers have a significant effect on the range but a minimal effect on the interquartile range (IQR).
Hint: Consider how the range is calculated (min to max) versus how the IQR is calculated (middle 50% of data).
Q6.medium
A box plot is drawn for a set of data. The left whisker extends to 10, the left edge of the box is at 15, the line inside the box is at 20, the right edge of the box is at 28, and the right whisker extends to 35. What is the interquartile range (IQR) of this data?
1. A)10
2. B)13
3. C)15
4. D)25
Show answer
Answer: 13
Hint: Recall that a box plot visually represents the five-number summary: minimum, Q1, median (Q2), Q3, and maximum. The box itself represents the middle 50% of the data.
Q7.hard
A box plot represents the scores of students in a math test. The minimum score is 30, Q1 is 50, the median is 65, Q3 is 80, and the maximum score is 95. Which of the following statements about the test scores *must be false*?
1. A)A) At least 25% of students scored between 65 and 80.
2. B)B) The range of scores is 65.
3. C)C) More students scored between 50 and 65 than between 80 and 95.
4. D)D) The middle 50% of scores span 30 marks.
Show answer
Answer: C) More students scored between 50 and 65 than between 80 and 95.
Hint: Recall that a box plot divides the data into four equal parts, each representing 25% of the observations.
Q8.hard
A cumulative frequency curve (ogive) shows the heights of 100 plants. The cumulative frequency for a height of 20 cm is 10, for 30 cm is 40, for 40 cm is 70, and for 50 cm is 90. Estimate the interquartile range (IQR) of plant heights, assuming linear interpolation within the intervals.
1. A)A) 10 cm
2. B)B) 15 cm
3. C)C) 18 cm
4. D)D) 20 cm
Show answer
Answer: C) 18 cm
Hint: Determine the data points for Q1 (25th percentile) and Q3 (75th percentile) first. Then, use linear interpolation within the given intervals to estimate their values.
Q9.hard
Ravi was asked to find the interquartile range (IQR) for the dataset: `5, 8, 12, 15, 18, 20, 22`. He found the median to be 15. Then, he took the lower half as `5, 8, 12, 15` and calculated Q1 as the median (average of 8 and 12, which is 10). He took the upper half as `15, 18, 20, 22` and calculated Q3 as the median (average of 18 and 20, which is 19). He concluded IQR = 19 - 10 = 9. What was Ravi's mistake?
1. A)A) The median calculation was incorrect.
2. B)B) He included the overall median (15) in both halves when calculating Q1 and Q3.
3. C)C) The dataset should have been arranged in descending order.
4. D)D) He used an incorrect formula for IQR.
Show answer
Answer: B) He included the overall median (15) in both halves when calculating Q1 and Q3.
Hint: Consider the rule for dividing a dataset into halves for quartile calculation when the total number of data points is odd.

These are 9 of the 59 questions available for Statistics (Measures of Spread). Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.