It may be easier to calculate the mean, median, and mode if you rearrange the numbers first.
Mean = 11.1
Median = 11.3
Mode = 13.4
Best measure: Mean or Median
Practice makes perfect
We are given the following data set.
13.4, 13.1, 10.4, 6.8, 11.4, 10.8, 13.4, 11.3, 9.3
The first thing that should be done when finding the key features of a data set is rearranging the numbers from least to greatest.
6.8, 9.3, 10.4, 10.8, 11.3, 11.4, 13.1, 13.4, 13.4Let's proceed to finding the mean, median, and mode.
Mean
The mean of a data set is calculated by finding the sum of all values in the set and then dividing by the number of values in the set. In this case, there are 9 values in the set.
To identify the median, we observe the middle value.
6.8, 9.3, 10.4, 10.8, 11.3, 11.4, 13.1, 13.4, 13.4
We can see that the middle value in this set is 11.3, so this is our median.
Mode
The mode of a data set is the value that occurs most frequently.
6.8, 9.3, 10.4, 10.8, 11.3, 11.4, 13.1, 13.4, 13.4
We can see that 13.4 occurs more frequently than any other value in the set, so this is the mode.
Which Measure Is Best?
Here, the mode is only repeated twice and is the greatest number. Therefore, it is not a good measure.
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Mode & Mean & Median
* & ? & ?
Keep in mind that outliers affect the mean but not the median. Since 6.8 is much less than the rest of the values, we can consider it as an outlier. Therefore, in this case, the best measure is the median. However, the difference between the mean 1 and the median 11.3 is not that large. This means that another good measure could be the mean.
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Mode & Mean & Median
* & ✓ & ✓
