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Interpreting standard deviation - MYP Questionbank | RevisionDojo

Practice Interpreting 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

Determine whether the following statement is true or false:

"Standard deviation is best interpreted as the 'typical distance' of data values from the mean, rather than the absolute range between the highest and lowest values."

Question 6

To compute the population standard deviation $\sigma$ using the formula

\sigma = \sqrt{\frac{\sum x^2}{n} - \mu^2}

which of the following pieces of information is required to determine the value of $\mu$ ?

Question 7

A dataset representing the daily commute times of $25$ employees has a mean $\mu = 40\text{ minutes}$ and a standard deviation $\sigma = 10\text{ minutes}$ . If $5$ additional employees are included in the survey, and all of them have a commute time of exactly $40\text{ minutes}$ , which of the following statements best describes the effect on the dataset?

Question 8

Alice scored 85 on a math test with $\mu = 75$ and $\sigma = 5$ . Bob scored 80 on a science test with $\mu = 70$ and $\sigma = 10$ . Which statement correctly compares their relative performance?

Question 9

For a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ , what is the approximate percentage of data values that lie within the interval $[\mu - 3\sigma, \mu - \sigma]$ ?

Question 10

A hiker's daily distances, $x$ km, are recorded for 10 days, where $\sum x = 150$ and $\sum x^2 = 2340$ . Calculate the population standard deviation, $\sigma$ , and determine the range of distances that are within one standard deviation of the mean.

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

Determine whether the following statement is true or false:

"Standard deviation is best interpreted as the 'typical distance' of data values from the mean, rather than the absolute range between the highest and lowest values."

Question 6

To compute the population standard deviation $\sigma$ using the formula

\sigma = \sqrt{\frac{\sum x^2}{n} - \mu^2}

which of the following pieces of information is required to determine the value of $\mu$ ?

Question 7

Question 8

Alice scored 85 on a math test with $\mu = 75$ and $\sigma = 5$ . Bob scored 80 on a science test with $\mu = 70$ and $\sigma = 10$ . Which statement correctly compares their relative performance?

Question 9

For a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ , what is the approximate percentage of data values that lie within the interval $[\mu - 3\sigma, \mu - \sigma]$ ?

Question 10

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

Determine whether the following statement is true or false:

"Standard deviation is best interpreted as the 'typical distance' of data values from the mean, rather than the absolute range between the highest and lowest values."

Question 6

To compute the population standard deviation $\sigma$ using the formula

\sigma = \sqrt{\frac{\sum x^2}{n} - \mu^2}

which of the following pieces of information is required to determine the value of $\mu$ ?

Question 7

Question 8

Alice scored 85 on a math test with $\mu = 75$ and $\sigma = 5$ . Bob scored 80 on a science test with $\mu = 70$ and $\sigma = 10$ . Which statement correctly compares their relative performance?

Question 9

For a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ , what is the approximate percentage of data values that lie within the interval $[\mu - 3\sigma, \mu - \sigma]$ ?

Question 10

Interpreting standard deviation Questionbank