Question

The data set gives the number of bottles filled by each of the workers in a bottling plant in one day.

Answer 1

Before we can determine which measure of central tendency is the best we need to determined whether data set is skewed or not.

We can determine the skewness, if we know at least the median and the mean.

The array of the above data set is,

$16,18,28,29,35,36,37,38,40,41,44,66,68,72$

The Median of the above array is

$\frac{37 + 38}{2} = \frac{75}{2} = 37.5$

The mean is

$\frac{16 + 18 + 28 + 29 + 35 + 36 + 37 + 38 + 40 + 41 + 44 + 66 + 68 + 72}{14} = \frac{532}{14} = 38$

Since the mean and the median are not the same, the distribution is skewed.

$For a skewed distribution, the best measure of central tendency is the median.$

To one decimal place, the median is;

$37.5$

NB: If the distribution is not skewed then it is normal. In a normal distribution the median is equal to the mean. The mode is considered the best measure of center in this case.

Answer 2

The best measure of center for this data set is the median

its value expressed up to one decimal place is 37.5