Find the mean and the median, and compare them to the data values. Which one do you think represents the tendency of these values more accurately?
The median. See solution for details.
Practice makes perfect
To decide which measures of center work best to represent the tendency of the values from Example 1B, we will calculate both the mean and the median. Then, we will compare them with the set values to decide which one is more accurate for this case.
Finding the mean
Recall that the mean is the sum of the values in the set divided by the number of values in the set. In this case, we have the values shown below.
$75, $97, $360, $84, $119, $100
First, we need to find the sum of these values.
1 75+2 97+3 360+4 84+5 119+ 6 100 = 835
Now we find the mean dividing by the total by the number of values. In this case, we have 6 values.
&Mean
835/6=139.1&666... ≈ 139.17
Finding the median
The median is the middle value in a set when the values are arranged in numerical order. The first thing to do is rearrange our values.
$75, $97, $360, $84, $119, $100
75, 84, 97, 100, 119, 360
Notice that since we have an even number of values, we have two middle values. In cases like this, we average these middle values to find the median.
Median
97+100/2=98.5
Conclusion
Notice that the mean value is too high, since 139.17 is above all the set values but 360. This is because the value 360 is very large in comparison with the rest of the values, and this make the data inconsistent. In this case, the mean value 98.5 is more accurate for representing the tendency of the whole set of values.
