Question

The number of passengers travelling by a bus on different days of a week are recorded as below:


What will be the three measures of central tendency?

• A. $\text{Mean}=\text{Median}=\text{Mode}$
• B. $\text{Mean}=\text{Median}=99$, $\text{No mode}$
• C. $\text{Mean}=99,\text{Median}=\text{Mode}=105$
• D. $\text{Mean}=105,\text{Median}=99,\text{Mode}=92$

Answer 1

The correct option is B $\text{Mean}=\text{Median}=99$, $\text{No mode}$

When the data set is arranged in ascending order, then the middle value is said to be the median of the data set.

Arrange the given data set in ascending order and observe the middle value.


Since, the middle value of given data is $99$, therefore the median is $99$.

The mean of the data set is calculated as follows,

$\begin{array}{cc}\text{Mean}& =\frac{\text{Sum of all data points}}{\text{Total number of data points}}\\ & =\frac{100+98+102+99+97+105+92}{7}\\ & =\frac{693}{7}\\ & =99\end{array}$

Thus, the mean of the given data is $99$.

Now, observe the given data set, since all the values occur only once, therefore the given data set is said to have no mode.

Hence, the given data set has same mean and median, while it has no mode.