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HiSET: Math : Summarizing numerical data sets

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Example Question #21 : Data Analysis, Probability, And Statistics

Consider the data set:

$\left \{ 12, 15, 17, 19, 19, 19, 22, 23, 23 \right \}$

Which is true of the arithmetic mean $\mu$ , the median , and the midrange ?

Possible Answers:

$m < \mu < M$

$\mu < m <M$

$m< M < \mu$

$M < m < \mu$

$M < \mu < m$

Correct answer:

$m < \mu < M$

Explanation:

The mean of a data set is equal to the sum of the entries divided by the number of entries. There are nine entries in the set, so

$\mu =( 12+15+ 17+ 19+ 19+ 19+ 22+ 23+ 23 ) \div 9 = 169 \div 9 \approx 18.8$

The median of a data set with an odd number of values is the value of the entry in the middle when the values are arranged in ascending order:

$\left \{ 12, 15, 17, 19, \textbf{19}, 19, 22, 23, 23 \right \}$

This value is M = 19 .

The midrange of a data set is the arithmetic mean of the least and greatest elements in the set. This element is

$m = (12+23)\div 2 = 17.5$

The correct response is that

$m < \mu < M$ .

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Example Question #11 : Use Measures Of Center To Draw Inferences About Populations

Which of the following is an example of a set with no mode?

Possible Answers:

$\left \{ 70, 72, 74, 76, 77, 81, 83, 85, 89, 92 \right \}$

All of the sets in the other four choices are examples of sets with no mode.

$\left \{ 70, 70,70, 70,70, 92 , 92 , 92 , 92 , 92 \right \}$

$\left \{ 70, 70, 74, 74, 81, 81, 83, 83, 92 , 92 \right \}$

$\left \{ 81, 81, 81, 81, 81, 81, 81, 81, 81, 81\right \}$

Correct answer:

$\left \{ 70, 72, 74, 76, 77, 81, 83, 85, 89, 92 \right \}$

Explanation:

The mode of a data set is the value that appears in the set the most frequently (or a mode is one of several such values). A set is considered to have no mode if and only if no value is repeated. Of the four data sets given, $\left \{ 70, 72, 74, 76, 77, 81, 83, 85, 89, 92 \right \}$ is the only one that fits this definition.

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HiSET: Math : Summarizing numerical data sets

Study concepts, example questions & explanations for HiSET: Math

All HiSET: Math Resources

Example Questions

Example Question #21 : Data Analysis, Probability, And Statistics

Example Question #11 : Use Measures Of Center To Draw Inferences About Populations

All HiSET: Math Resources

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