Calculation of measures of center - HiSet: High School Equivalency Test: Math

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Question

Find the mean of the following data set:

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

Answer

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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Question

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?

Answer

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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Question

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?

Answer

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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