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

The correct option is D

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

Explanation of correct option:

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

Arrange the data set $4,3,4,3,4,6,4$ in ascending order:

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

The median is the middle value of the ordered data set.

So, the median of the set (D) is 4.

Mode the is the data value that repeats with maximum frequency.

So, the mode of data set (D) is 4.

Mean is the sum of data values divided by the number of data values.

$\begin{array}{rcl}\frac{3+3+4+4+4+4+6}{7}& =& \frac{28}{7}\\ & \Rightarrow & \mathrm{mean}=4\end{array}$

So, the mean of data set (D) is 4.

Thus, the mean, median , and mode of the data in option (D) is 4.

So, option (D) is the correct option.

Explanation of incorrect options:

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

Arrange the data set $6,2,5,4,3,4,1$ in ascending order:

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

The middle value of the ordered data is 4.

So, the median of the data set (A) is 4.

The value 4 is repeated the most number of times.

So, the mode of the data set (A) is also 4.

Find the mean of the data:

$\begin{array}{rcl}\frac{1+2+3+4+4+5+6}{7}& =& \frac{25}{7}\\ & \Rightarrow & \mathrm{mean}=\frac{25}{7}\end{array}$

So, the mean of the data set (A) is not 4.

Thus, option (A) is incorrect.

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

Arrange the data set $4,2,2,1,3,2,3$ in ascending order:

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

The middle value of the ordered data is 2.

So, the median of the data set (B) is 2.

The value 2 is repeated the most number of times.

So, the mode of the data set (B) is also 2.

Find the mean of the data:

$\begin{array}{rcl}\frac{1+2+2+2+3+3+4}{7}& =& \frac{17}{7}\\ \therefore \mathrm{Mean}& =& \frac{17}{7}\end{array}$

So, the mean of the data set (B) is not 4.

Thus, option (B) is incorrect.

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

Arrange the data set $2,3,7,3,8,3,2$ in ascending order:

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

The middle value of the ordered data is 3.

So, the median of the data set (C) is 3.

The value 2 is repeated the most number of times.

So, the mode of the data set (C) is also 2.

The median and mode of the data set (C) is not equal.

Thus, option (C) is also incorrect.

From the obtained values, it is observed that only the data set (D) has equal values of mean, median, and mode, that is 4.

Hence, the correct option is (D).