How many practice questions are available for Statistics (Standard Deviation)?

SparkEd Math offers 60+ practice questions for Statistics (Standard Deviation) across 3 difficulty levels (Easy, Medium, Hard) plus a timed test mode. Each question comes with visual step-by-step solutions and AI coaching hints.

Is Statistics (Standard Deviation) content free on SparkEd Math?

Yes! All Statistics (Standard Deviation) content on SparkEd Math is 100% free, including practice questions, visual solutions, lessons, and AI coaching. No credit card required.

How does SparkEd Math teach Statistics (Standard Deviation) differently from textbooks?

SparkEd Math uses visual step-by-step solutions for every Statistics (Standard Deviation) problem, making complex concepts easy to understand. The platform includes 3 difficulty levels for progressive learning, a Super Power Help AI coach for instant doubt-clearing, and interactive practice rather than passive reading.

Is SparkEd's Statistics (Standard Deviation) content aligned with the IB syllabus?

Yes, all Statistics (Standard Deviation) questions and lessons on SparkEd Math are fully aligned with the International Baccalaureate (MYP) (IB) syllabus for Class 10. The content follows the official curriculum structure and exam pattern.

Statistics (Standard Deviation) — Class 10 IB (2025-26)

About Statistics (Standard Deviation) — Class 10 IB

Calculate variance and standard deviation; compare data sets using statistical measures. This topic is part of the IB Class 10 mathematics syllabus (chapter: Unit 7). 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.

Statistics (Standard Deviation) — solved examples for Class 10 IB

Example 1easy

Which of the following statements BEST describes what the standard deviation measures?

A)The central tendency of the data.
B)The highest value in the data set.
C)The average amount by which data points deviate from the mean.
D)The difference between the highest and lowest values.

Step-by-step solution

The standard deviation is a fundamental measure of dispersion or spread in a dataset.
It quantifies the typical amount or average distance by which individual data points deviate from the mean (average) of the dataset.
A smaller standard deviation indicates that data points are clustered more closely around the mean, while a larger one indicates wider spread.

Answer: The average amount by which data points deviate from the mean.

Example 2medium

Calculate the standard deviation for the following set of numbers: 2, 4, 6, 8, 10.

A)√8
B)√10
C)2√2
D)2√5

Step-by-step solution

1. Calculate the mean (μ): μ = (2 + 4 + 6 + 8 + 10) / 5 = 30 / 5 = 6.
2. Calculate the squared deviations from the mean: (2-6)²=16, (4-6)²=4, (6-6)²=0, (8-6)²=4, (10-6)²=16.
3. Calculate the variance (σ²): Sum of squared deviations / N = (16 + 4 + 0 + 4 + 16) / 5 = 40 / 5 = 8.
4. Calculate the standard deviation (σ): σ = √Variance = √8.

Answer: √8

Example 3hard

A dataset consists of five observations: 2, 4, 6, x, 10. If the standard deviation of this dataset is √8, what are the possible values of x?

A)A) 3 or 8
B)B) 2 or 9
C)C) 4 or 7
D)D) 5 or 6

Step-by-step solution

Calculate the mean (μ): μ = (2 + 4 + 6 + x + 10) / 5 = (22 + x) / 5.
Given SD = √8, so Variance (σ²) = 8.
Use the alternative variance formula: σ² = (Σx_i² / n) - μ². First, calculate Σx_i² = 2² + 4² + 6² + x² + 10² = 4 + 16 + 36 + x² + 100 = 156 + x².
Substitute into the variance formula: 8 = [(156 + x²) / 5] - [(22 + x) / 5]². Multiply by 25 to clear denominators: 200 = 5(156 + x²) - (22 + x)². Simplify to 200 = 780 + 5x² - (484 + 44x + x²), which leads to 4x² - 44x + 96 = 0. Dividing by 4 gives x² - 11x + 24 = 0. Factoring yields (x - 3)(x - 8) = 0. Thus, x = 3 or x = 8.

Answer: A) 3 or 8

Practice questions on Statistics (Standard Deviation)

Q1.easy
A dataset of students' test scores has a mean of 75 and a standard deviation of 8. If 5 bonus marks are added to every student's score, what will be the new standard deviation?
1. A)3
2. B)8
3. C)13
4. D)70
Show answer
Answer: 8
Hint: Consider how adding a constant value to every data point affects the spread of the data, not just its center.
Q2.easy
The variance of a dataset is 25. What is its standard deviation?
1. A)5
2. B)25
3. C)625
4. D)0.04
Show answer
Answer: 5
Hint: Recall the fundamental mathematical relationship between variance and standard deviation.
Q3.easy
If the standard deviation of a dataset is 0, what does this imply about the data points?
1. A)All data points are widely spread out.
2. B)There is at least one outlier in the dataset.
3. C)The mean of the dataset is also 0.
4. D)All data points in the dataset are identical.
Show answer
Answer: All data points in the dataset are identical.
Hint: Consider what it means for there to be absolutely no deviation from the mean for any data point.
Q4.medium
Two factories, A and B, produce light bulbs. Factory A has a mean bulb life of 1200 hours with a standard deviation of 50 hours. Factory B has a mean bulb life of 1250 hours with a standard deviation of 150 hours. Which factory produces more consistent light bulbs?
1. A)Factory A
2. B)Factory B
3. C)Both are equally consistent
4. D)Cannot be determined
Show answer
Answer: Factory A
Hint: A smaller standard deviation indicates less variability and thus more consistency in the data.
Q5.medium
The standard deviation of a set of 5 observations is 3. If each observation in the set is increased by 7, what will be the new standard deviation?
1. A)3
2. B)10
3. C)21
4. D)49
Show answer
Answer: 3
Hint: Think about how adding a constant to every data point affects the spread of the data.
Q6.medium
A data set has a variance of 16. If each observation in the data set is multiplied by 3, what will be the new standard deviation?
1. A)4
2. B)12
3. C)36
4. D)48
Show answer
Answer: 12
Hint: If each observation is multiplied by a constant 'k', the new standard deviation will be 'k' times the original standard deviation.
Q7.hard
A dataset of 10 observations has a mean of 15 and a variance of 9. If each observation in the dataset is first multiplied by 2, and then 5 is subtracted from each result, what will be the new standard deviation?
1. A)A) 3
2. B)B) 6
3. C)C) 13
4. D)D) 18
Show answer
Answer: B) 6
Hint: Remember that multiplying each observation by a constant scales the standard deviation, but adding or subtracting a constant does not change the standard deviation.
Q8.hard
Two cricket players, Rohit and Virat, have scored the following runs in 10 matches each. Rohit: Mean = 50 runs, Standard Deviation = 8 runs. Virat: Mean = 60 runs, Standard Deviation = 12 runs. Which player is generally considered more consistent in their batting performance, and why?
1. A)A) Rohit, because his standard deviation is lower.
2. B)B) Virat, because his mean score is higher.
3. C)C) Rohit, because his Coefficient of Variation is lower.
4. D)D) Virat, because his standard deviation is higher, indicating more varied skills.
Show answer
Answer: C) Rohit, because his Coefficient of Variation is lower.
Hint: When comparing consistency between datasets with different means, simply comparing standard deviations can be misleading. Consider a relative measure of dispersion that accounts for the mean.
Q9.hard
A researcher calculated the standard deviation of 10 observations as 5. However, it was later discovered that one observation, which was initially recorded as 15, should have been 20. If the mean of the original 10 observations was 30, what is the corrected standard deviation?
1. A)A) √10.25
2. B)B) √12.25
3. C)C) √14.25
4. D)D) √16.25
Show answer
Answer: B) √12.25
Hint: You'll need to recalculate the sum of observations (Σx) and the sum of squared observations (Σx²) after correcting the error, then compute the new mean and variance.

These are 9 of the 60 questions available for Statistics (Standard Deviation). Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.