Question

In which of the following data set(s) all the measures of central tendency are same?

• A. $\{1,6,6,11\}$
• B. $\{2,3,3,3,4\}$
• C. $\{0,6,6,6\}$
• D. None of the above.

Answer 1

Answer: (A), (B)

$\{2,3,3,3,4\}$

The measures of central tendency are mean, median and mode.
Here, all data sets are arranged in ascending order.

Consider each data set one by one.

• $\{1,6,6,11\}$

Mean $=\frac{1+6+6+11}{4}=\frac{24}{4}=6$

For even-numbered data set,
Median = Average of second and third data points
$\Rightarrow$ Median $=\frac{6+6}{2}=6$

Mode is the data point with highest frequency, i.e., 6
$\therefore$ For this data set, mean, median and mode are equal.

• $\{2,3,3,3,4\}$

Mean $=\frac{2+3+3+3+4}{5}=\frac{15}{5}=3$

For odd-numbered data set, median is the middle data point when the data set is arranged in ascending/ descending order, i.e., 3

The number three appears thrice. It's a data point with maximum frequency. Hence, mode is 3.
$\therefore$ This is also the correct option.

• $\{0,6,6,6\}$

Mean $=\frac{0+6+6+6}{4}=\frac{18}{4}=4.5$
Median = Average of second and third data points
$\Rightarrow$ Median $=\frac{6+6}{2}=6\ne$ Mean
$\therefore$ This is a wrong option.