Question

QuestionThe following is a data set of the average weekly number of cups of coffee consumed by employees in an office. Find the mean and median and determine if the mean or median is the better measure of central tendency.5,0,5,2,0,10,7,8,10,21,5,8,2,5,3,5Select the correct answer below:Mean = 5, Median = 6The median is the better measure of central tendency.Mean = 5, Median = 6The mean is the better measure of central tendency.Mean = 6, Median = 5The median is the better measure of central tendency.Mean = 6, Median = 5The mean is the better measure of central tendency.

Answer 1

Explanation

we will begin by finding the mean and median of the data set

The mean is simply the average of the set, which will be

$mean=\frac{5+0+5+2+0+10+7+8+10+21+5+8+2+5+3+5}{16}=\frac{96}{16}=6$

The median is

$\begin{gathered} \mathrm{The\:median\:is\:the\:value\:separating\:the\:higher\:half\:of\:the\:data\:set,\:from\:the\:lower\:half.} \\ \mathrm{If\:the\:number\:of\:terms\:is\:odd,\:then\:the\:median\:is\:the\:middle\:element\:of\:the\:sorted\:set} \\ If\:the\:number\:of\:terms\:\:is\:even,\:then\:the\:median\:is\:the\:arithmetic\:mean\:of\:the\:two\:middle\:elements\:of\:the\:sorted\:set \end{gathered}$

Thus, we have the median as 5

To check which is a better measure, we will have to check the skewness

The skew value is 1.51

This means it is positively skewed

Thus

If the distribution is positively skewed then the mean is greater than the median which is in turn greater than the mode.

Therefore, the answer is