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HiSET: Math : Use measures of center to draw inferences about populations

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Example Questions

Example Question #22 : 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:

$m < \mu < M$

$M < \mu < m$

$m< M < \mu$

$\mu < m <M$

$M < m < \mu$

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 : Summarizing Numerical Data Sets

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

Possible Answers:

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

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

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

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

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

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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Example Question #1 : Calculation Of Measures Of Center

Find the mean of the following data set:

$10,\ 12,\ 3,\ 4,\ 7,\ 8,\ 9,\ 10,\ 12,\ 11,\ 13,\ 14,\ 16, \textup{ and } 18$

Possible Answers:

14.5

147

10.5

11.5

Correct answer:

10.5

Explanation:

The mean is found by adding the values in a set and dividing that number by the total number of values.

$\textup{Mean}=\frac{10+12+3+4+7+8+9+10+12+11+13+14+16+18}{14}$

$\textup{Mean}=\frac{147}{14}$

$\textup{Mean}=10.5$

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Example Question #31 : Data Analysis, Probability, And Statistics

Consider the data set

$\left \{ 10, 12, 12, 12, 12, 13, 16, 17, 20 \right \}$

Of the mean, the median, the mode, and the midrange of the data set, which two are equal?

Possible Answers:

The mean and the mode

The midrange and the mode

The median and the midrange

The median and the mode

The mean and the midrange

Correct answer:

The median and the mode

Explanation:

The mean of a data set $\overline{x}$ is equal to the sum of the terms divided by the number of terms, which here is 9. Therefore,

$\overline{x} = \frac{ 10+ 12+ 12+ 12+12+ 13+ 16+ 17+ 20}{9} = \frac{129}{9} \approx 13.8$

The median of a data set with an odd number of terms is the term that falls in the middle when the terms are ordered. The terms are already ordered:

$\left \{ 10, 12, 12, 12, \textbf{12}, 13, 16, 17, 20 \right \}$

so the element that falls in the middle is 12.

The mode of the data set is the term that occurs most frequently, which is 12.

The midrange is the mean of the least and greatest elements, which is

$\frac{10+20}{2} = \frac{30}{2} = 15$ .

Of the four - mean, median, mode, and midrange - the median and the mode are equal.

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Example Question #2 : Calculation Of Measures Of Center

Consider the data set

$\left \{ 10, 12, 12, 12, 12, 13, 16, 17, 20 \right \}$

Of the mean, the median, the mode, and the midrange of the data set, which is the least?

Possible Answers:

The median is the least of the four.

The median and the mode tie for being the least of the four.

The median and the midrange tie for being the least of the four.

The midrange is the least of the four.

The mode is the least of the four.

Correct answer:

The median and the mode tie for being the least of the four.

Explanation:

The mean of a data set $\overline{x}$ is equal to the sum of the terms divided by the number of terms, which here is 9. Therefore,

$\overline{x} = \frac{ 10+ 12+ 12+ 12+12+ 13+ 16+ 17+ 20}{9} = \frac{129}{9} \approx 13.8$

The median of a data set with an odd number of terms is the term that falls in the middle when the terms are ordered. The terms are already ordered:

$\left \{ 10, 12, 12, 12, \textbf{12}, 13, 16, 17, 20 \right \}$

so the element that falls in the middle is 12.

The mode of the data set is the term that occurs most frequently, which is 12.

The midrange is the mean of the least and greatest elements, which is

$\frac{10+20}{2} = \frac{30}{2} = 15$ .

Of the four - mean, median, mode, and midrange - the median and the mode tie for being the least.

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HiSET: Math : Use measures of center to draw inferences about populations

Study concepts, example questions & explanations for HiSET: Math

All HiSET: Math Resources

Example Questions

Example Question #22 : Data Analysis, Probability, And Statistics

Example Question #11 : Summarizing Numerical Data Sets

Example Question #1 : Calculation Of Measures Of Center

Example Question #31 : Data Analysis, Probability, And Statistics

Example Question #2 : Calculation Of Measures Of Center

All HiSET: Math Resources

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