Measures of Dispersion

Math ⇒ Statistics and Probability

Measures of Dispersion starts at 8 and continues till grade 12. QuestionsToday has an evolving set of questions to continuously challenge students so that their knowledge grows in Measures of Dispersion. How you perform is determined by your score and the time you take. When you play a quiz, your answers are evaluated in concept instead of actual words and definitions used.

See sample questions for grade 11

A data set has a mean of 15 and a standard deviation of 0. What are the possible values in the data set?

A data set has a variance of 16. What is its standard deviation?

A data set has the following values: 10, 12, 14, 16, 18. What is the mean absolute deviation?

A sample of 5 numbers has a mean of 10 and the following values: 8, 9, 10, 11, 12. What is the variance?

Calculate the interquartile range for the data set: 3, 7, 8, 12, 13, 14, 18, 21, 23.

Calculate the range for the following data set: 5, 8, 12, 20, 25.

Calculate the standard deviation for the data set: 2, 4, 4, 4, 5, 5, 7, 9.

Calculate the variance for the data set: 2, 4, 4, 4, 5, 5, 7, 9.

Describe a situation where the range is a misleading measure of dispersion.

Describe how the standard deviation changes if each value in a data set is increased by a constant.

Explain the difference between variance and standard deviation.

Explain why the interquartile range is considered a resistant measure of dispersion.

If the standard deviation of a data set is 0, what can you say about the data?

Which measure of dispersion divides the data into four equal parts?

Which measure of dispersion is defined as the average of the absolute differences between each data value and the mean?

A data set consists of the following values: 15, 22, 20, 18, 25, 30, 17. If the value 100 is added to the data set, which measure of dispersion will be most affected?

A teacher records the scores of two classes on a test. Class A has a standard deviation of 5, while Class B has a standard deviation of 10. Both classes have the same mean. What can you infer about the consistency of the scores in the two classes?

Explain why the standard deviation is preferred over the range as a measure of dispersion for comparing two data sets with similar means but different spreads.

Given the data set: 4, 8, 6, 5, 3, 7, 9, calculate the coefficient of variation (CV) and interpret its meaning.

If every value in a data set is multiplied by a constant k, how does the variance change?