Question

For which set of data will the mean, the median, and the mode all be equal?

• A. $1,2,2,3,7$
• B. $1,1,1,2,5$
• C. $1,2,5,5,12$
• D. $1,2,5,5,7$

Answer 1

The correct option is C $1,2,5,5,12$

$\text{A. Mean =}\frac{\text{sum of the observations}}{\text{number of observations}}=\frac{1+2+5+5+7}{5}=4$
The observations are in ascending order. Since the number of observations is odd, the median is the middle value.
$1,2,5,5,7$
Median $=5$
Mode $=5$
$\text{B. Mean =}\frac{\text{sum of the observations}}{\text{number of observations}}=\frac{1+1+1+2+5}{5}=2$
The observations are in ascending order. Since the number of observations is odd, the median is the middle value.
$1,1,1,2,5$
Median $=1$
Mode $=1$
$\text{C. Mean =}\frac{\text{sum of the observations}}{\text{number of observations}}=\frac{1+2+5+5+12}{5}=5$
The observations are in ascending order. Since the number of observations is odd, the median is the middle value.
$1,2,5,5,12$
Median $=5$
Mode $=5$
$\text{D. Mean =}\frac{\text{sum of the observations}}{\text{number of observations}}=\frac{1+2+2+3+7}{5}=3$
The observations are in ascending order. Since the number of observations is odd, the median is the middle value.
$1,2,2,3,7$
Median $=2$
Mode $=3$
The mean, median, and mode are the same for option C.