HiSET - Calculation of measures of center

Find the mean of the following data set:

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

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

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

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

$\textup{Mean}=10.5$

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?

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

The mode is the least of the four.

The midrange is the least of the four.

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

The median is the least of the four.

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.

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?

The median and the mode

The median and the midrange

The midrange and the mode

The mean and the mode

The mean and the midrange