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Variation and Standard Deviation - MYP Questionbank | RevisionDojo

Practice Variation and Standard Deviation with authentic MYP MYP Extended Mathematics exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of MYP examiners.

Type

Difficulty

Question 1

A distribution has $\mu = 100$ and $\sigma = 15$ . An observation of $x = 145$ is ________ standard deviations above the mean.

Question 2

Investment Fund X has an average annual return of $8\%$ with $\sigma = 2\%$ . Investment Fund Y has an average annual return of $10\%$ with $\sigma = 7\%$ . An investor who prioritizes 'minimizing risk and maximizing predictability' should choose:

Question 3

Which of the following best describes the relationship between the mean and standard deviation in a normal distribution?

Question 4

Consider the following statement regarding the $68-95-99.7$ rule:

'The $68-95-99.7$ rule is a universal property that can be applied to any data set, regardless of whether its distribution is symmetric or skewed.'

Which of the following correctly evaluates this statement?

Question 5

Why is the standard deviation often preferred over the variance for reporting the spread of data in a final conclusion?

Question 6

Group A contains 4 values with a sum of 40. Group B contains 6 values with a sum of 90. Calculate the combined mean $\mu_{1+2}$ of the two groups when merged.

Question 7

A researcher collects heights of 50 randomly selected students from a university of 10,000 students to estimate the variation in height for the whole university. Which measure of spread is most appropriate to report for this purpose?

Question 8

Calculate the population standard deviation $\sigma$ for the dataset $\{0, 10, 20\}$ .

Question 9

Calculate the sample standard deviation $s_{n-1}$ for the small sample $\{4, 10\}$ .

Question 10

If every value $x$ in a population data set is multiplied by a constant $k=2$ , how does the population variance $\sigma^2$ change?

Type

Difficulty

Question 1

A distribution has $\mu = 100$ and $\sigma = 15$ . An observation of $x = 145$ is ________ standard deviations above the mean.

Question 2

Question 3

Which of the following best describes the relationship between the mean and standard deviation in a normal distribution?

Question 4

Consider the following statement regarding the $68-95-99.7$ rule:

'The $68-95-99.7$ rule is a universal property that can be applied to any data set, regardless of whether its distribution is symmetric or skewed.'

Which of the following correctly evaluates this statement?

Question 5

Why is the standard deviation often preferred over the variance for reporting the spread of data in a final conclusion?

Question 6

Group A contains 4 values with a sum of 40. Group B contains 6 values with a sum of 90. Calculate the combined mean $\mu_{1+2}$ of the two groups when merged.

Question 7

Question 8

Calculate the population standard deviation $\sigma$ for the dataset $\{0, 10, 20\}$ .

Question 9

Calculate the sample standard deviation $s_{n-1}$ for the small sample $\{4, 10\}$ .

Question 10

If every value $x$ in a population data set is multiplied by a constant $k=2$ , how does the population variance $\sigma^2$ change?

Type

Difficulty

Question 1

A distribution has $\mu = 100$ and $\sigma = 15$ . An observation of $x = 145$ is ________ standard deviations above the mean.

Question 2

Question 3

Which of the following best describes the relationship between the mean and standard deviation in a normal distribution?

Question 4

Consider the following statement regarding the $68-95-99.7$ rule:

'The $68-95-99.7$ rule is a universal property that can be applied to any data set, regardless of whether its distribution is symmetric or skewed.'

Which of the following correctly evaluates this statement?

Question 5

Why is the standard deviation often preferred over the variance for reporting the spread of data in a final conclusion?

Question 6

Group A contains 4 values with a sum of 40. Group B contains 6 values with a sum of 90. Calculate the combined mean $\mu_{1+2}$ of the two groups when merged.

Question 7

Question 8

Calculate the population standard deviation $\sigma$ for the dataset $\{0, 10, 20\}$ .

Question 9

Calculate the sample standard deviation $s_{n-1}$ for the small sample $\{4, 10\}$ .

Question 10

If every value $x$ in a population data set is multiplied by a constant $k=2$ , how does the population variance $\sigma^2$ change?

Variation and Standard Deviation Questionbank