Question

Which of the following has the same mean, median and mode?

• A. $6$, $2$, $5$, $4$, $3$, $4$, $1$
• B. $4$,$2$,$2$, $1$,$3$,$2$,$3$
• C. $2$,$3$,$7$,$3$.$8$,$3$,$2$
• D. $4$,$3$,$4$,$3$.$4$.$6$,$4$

Answer 1

Answer: (D)

$4$,$3$,$4$,$3$.$4$.$6$,$4$

Option $A:6,2,5,4,3,4,1$

Arranging the numbers in ascending order we get,

$1,2,3,4,4,5,6$

$\Rightarrow$ $Mean=\frac{1+2+3+4+4+5+6}{7}=\frac{25}{7}=3.57$

$\Rightarrow$ The mode of a set of data values is the value that appears most often

$\Rightarrow$ Here, number $4$ occurs $2$ times, so mode is $4$

$\Rightarrow$ We know, median is a middle number.

$\Rightarrow$ Here, $4th$ number is middle number which is $4$.

$\therefore$ Median is $4$.

$\therefore$ Option $A$ does not have same mean, median and mode.

Option $B:4,2,2,1,3,2,3$

Arranging the numbers in ascending order we get,

$1,2,2,2,3,3,4$

$\Rightarrow$ $Mean=\frac{1+2+2+2+3+3+4}{7}=\frac{17}{7}=2.42$

$\Rightarrow$ The mode of a set of data values is the value that appears most often

$\Rightarrow$ Here, number $2$ occurs $3$ times, so mode is $2$

$\Rightarrow$ We know, median is a middle number.

$\Rightarrow$ Here, $4th$ number is middle number which is $2$.

$\therefore$ Median is $2$.

$\therefore$ Option $B$ does not have same mean, median and mode.

Option $C:2,3,7,3,8,3,2$

Arranging the numbers in ascending order we get,

$2,2,3,3,3,7,8$

$\Rightarrow$ $Mean=\frac{2+2+3+3+3+7+8}{7}=\frac{28}{7}=4$

$\Rightarrow$ The mode of a set of data values is the value that appears most often

$\Rightarrow$ Here, number $3$ occurs $3$ times, so mode is $3$

$\Rightarrow$ We know, median is a middle number.

$\Rightarrow$ Here, $4th$ number is middle number which is $3$.

$\therefore$ Median is $3$.

$\therefore$ Option $C$ does not have same mean, median and mode.

Option $D:4,3,4,3,4,6,4$

Arranging the numbers in ascending order we get,

$3,3,4,4,4,4,6$

$\Rightarrow$ $Mean=\frac{3+3+4+4+4+4+6}{7}=\frac{28}{7}=4$

$\Rightarrow$ The mode of a set of data values is the value that appears most often

$\Rightarrow$ Here, number $4$ occurs $4$ times, so mode is $4$

$\Rightarrow$ We know, median is a middle number.

$\Rightarrow$ Here, $4th$ number is middle number which is $4$.

$\therefore$ Median is $4$.

$\therefore$ Option $D$ have same mean, median and mode.