Statistics

Statistics

The 2nd step is to determine which value is the middle value. You can easily do this by counting evenly from both ends.

----------------------- ----------------------- 28, 30, 31, 31, 33, 33, 33, 35, 36, 37, 42

For our data set, we have 11 values so we can count five from each end. Our middle value, or median, is 33. The works for all data sets with an odd number of observations. But, what if we have an even number of observations? Let us look at the following data set:

28, 30, 31, 31, 33, 33, 33, 35, 36, 37, 38, 42

Now we have 12 observations, so there is no one middle value. In this example, we need to take the average of the 2 middle values. As in the number set above, we count evenly from both sides.

----------------------- ----------------------- 28, 30, 31, 31, 33, 33, 33, 35, 36, 37, 38, 42

For this data set, we count five from each end. We then add the two middle values and divide by 2. This calculates the average of the middle values. For this example, the median would be 33+33 2 = 33 . Mode: The mode is the most commonly occurring number in a given data set. The mode can give important information about the randomness of a given data set, and therefore the strength of the experimental design, which we will cover latter in the text. It is important to note that a data set can have more than one mode. Let us look at our original data set:

Student ages: 31, 33, 30, 31, 35, 33, 36, 28, 42, 37, 33

The 1st step is to order the data set, just like we did for the median. This allows you to better visualize and identify repeating numbers. Our ordered data set is:

28, 30, 31, 31, 33, 33, 33, 35, 36, 37, 42

The 2nd step is to identify repeating numbers.

28, 30, 31, 31, 33, 33, 33, 35, 36, 37, 42

From the above data set, we have two sets of repeating numbers; the age 31 occurs twice and the age 33 occurs three times. So, the mode for the given data set is 33, because it occurs most often. We can interpret this as saying 3 out of 11 students is 33 years old.

But what if the data set changes to the following?

28, 30, 31, 31, 31, 33, 33, 33, 35, 36, 37, 42

Now we have three students who are 31 and three who are 33. Therefore, we have two modes and we would say that the mode of our population is 31 and 33. Remember, you can always have more than one mode if two sets of numbers appear an equal time in a given data set.

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