Question

The following data depicts the modes of public transportation used by various groups of people between two cities:
Mode of Transportation Bus Rental Car Train Metro Tram Number of passengers

$650$	$550$	$4900$	$850$	$700$

Which measure of central tendency represents the best value for number of passengers in public transportation?

• A. Mean
• B. Median
• C. Mode

Answer 1

The correct option is B Median

Let's find mean, mode and median one by one and compare the results for better understanding of suitable central tendency for the given data.

$\bullet \underset{–}{\text{Mean}}$

Mean/average

$=\frac{\text{Sum of all data points}}{\text{Total number of data points}}$

$=\frac{650+550+4900+850+700}{5}$

$=\frac{7650}{5}$

$=1530$

The average number of passengers ($1530$) in a public transportation is not close to other data points. Hence, the mean value is not the correct measure of central tendency for the given data.

$\bullet \underset{–}{\text{Mode}}$

In the given data set, the number of passengers in various public transportations are different, i.e., each data point occurs exactly once. Hence, the given data set has no mode.

$\bullet \underset{–}{\text{Median}}$

To determine the median, we first arrange the data points in ascending order.
Mode of Transportation Rental Car Bus Tram Metro Train Number of passengers

$550$	$650$	$700$	$850$	$4900$

The number in the middle position of the arranged data set is $700$, which corresponds to the number of passengers travelled by tram.

Here, $700$ is also quite closer to most of the other data points of the given data set.

$\therefore$ As compared to mean and mode, $\text{median}$ represents a better measure of central tendency for this particular data set.

$\underset{–}{\text{Note:}}$ An abnormal data compared to the rest of the data set is called an outlier. Here, in the given data set, train carries $4900$ passengers, which is very different from rest of the data points. So, we can call $4900$ as outlier in the given data set.