Question

Consider the following data set where “x” is a positive integer: {x+2, x+4, x-4, x-3, x+6} Which of the following statements are true? Select all that apply.A. The mode is x-4B. The median is x+2C. The mean is x+1D. None of above

Answer 1

Mode, median and mean

Initial step

Before start analyzing the mode, median and mean of the data set, we must organize it from lowest to highest:

{x+2, x+4, x-4, x-3, x+6}

↓

{x-4, x-3, x+2, x+4, x+6}

Mode

The mode is the most frequently repeated data. Since every data appears just one time, then this set has not mode.

Median

The median is the data that is in the center. We find it just by counting the same numbers from left to right and from right to left:

The median is x+2

Mean

The mean is given by the addition of all the data, and the division by the number of data.

there are 5 values, then we should divide their sum by 5:

`\begin{gathered} ((x-4)+(x-3)+(x+2)+(x+4)+(x+6))/(5) \\ =(x-4+x-3+x+2+x+4+x+6)/(5) \\ =(5x+5)/(5)=x+1 \end{gathered}`

The mean is x+1

ANSWERS: B and C