We are asked to determine which measure of central tendency would best represent the given set of data.
{ 4,1,5,5,6,8,9,5,5,3,2,7,5,5,1 }
First, let's try to visualize our data values.
Now, let's remember the different measures of central tendency.
We can start with the mode because, using our diagram, we can directly see that the most frequently occurring value for this data set is 5.
Next, to evaluate the median, we need to rearrange the values in our data set from least to greatest. Since we have 15 values in our data set, the median will be the middle value. In this case it is also 5.
{ 1,1,2,3,4,5,5, 5,5,5,5,6,7,8,9 }
Finally, let's evaluate the mean. To do this we will add all of the data values and divide this sum by the number of values, 15.
Let's summarize the measures of central tendency for this data set.
Measure
Value
Mean
≈ 4.73
Median
5
Mode
5
We could say that all of these measures are good because the data set is relatively symmetric. However, the mean could be considered as the best in this case because it shows that there are slightly more values that are less than 5.
