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

The correct answer is:

Mean = 6, Median = 5

The median is the better measure of central tendency.

To find the mean and median of the given data set:

Data set: 5, 0, 5, 2, 0, 10, 7, 8, 10, 21, 5, 8, 2, 5, 3, 5

Mean (Average):

Sum all the values and divide by the number of values.

(5 + 0 + 5 + 2 + 0 + 10 + 7 + 8 + 10 + 21 + 5 + 8 + 2 + 5 + 3 + 5) / 16

= 96 / 16

= 6

So, the mean is 6.

Median:

To find the median, first, you need to arrange the data in ascending order:

0, 0, 2, 2, 3, 5, 5, 5, 5, 7, 8, 8, 10, 10, 21

Since there are 16 data points, the median will be the average of the 8th and 9th values in this sorted list (or the middle two values):

Median = (5 + 5) / 2 = 10 / 2 = 5

So, the median is 5.

Now, to determine which measure of central tendency (mean or median) is better:

In this data set, we have some extreme values (like 21), which can significantly influence the mean. The mean is 6, which is somewhat pulled up by these extreme values.

The median, on the other hand, is 5, which is not affected by extreme values. It represents the middle value of the sorted data set and is a better measure of central tendency when dealing with data that might have outliers or extreme values.

Answer 2

Step-by-step 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=(5+0+5+2+0+10+7+8+10+21+5+8+2+5+3+5)/(16)=(96)/(16)=6`

The median is

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