This section tests your knowledge of statistical measures, probability, algorithms, and charts.
Here are some concepts you need to know.
Measures of Central Tendency
Measures of central tendency help us to determine how data is distributed. We will consider several measures of central tendency below.
The mean of a data set is average value of a data set. This can be found by adding together all of the values and dividing by the total number of values.
The mode of a data set is the value that occurs most frequently in the data set. It is possible to have more than one mode in a data set if several values occur the most.
The median of a data set is the middle value in the set. If there is an even number of data points, there will not be an exact middle. In this case, the median is found by taking the average of the two data points closest to the middle.
For example, suppose that the ages for a group of ten students were collected and are listed below:
9, 11, 13, 11, 8, 7, 13, 9, 9, 12
The mean of this data set can be found by adding all of these ages together and dividing by 10, since there are 10 students:
To find the mode and median of a data set, it is helpful to reorder the set from lowest to highest.
7, 8, 9, 9, 9, 11, 11, 12, 13, 13
Now we can see that the mode of the data set is 9 since 9 occurs 3 times, which is more than any other data point.
Since the data set has an even number of values, there are two values in the middle: 9 and 11. To find the median, you must average 9 and 11; therefore, the median of the data set is 10.
Common Features of a Data Set
Other common features of a data set that we consider are range and outliers.
The range of a data set is the difference between the largest value in the set and the smallest value in the set.
An outlier is a data point that is far outside of the normal range of data points. In other words, it is far away from all the other data.
For example, consider the list of speeds of cars on the highway below in miles per hour:
75, 70, 83, 42, 72, 81, 75, 80, 76, 69, 68
First, reorder the set from least to greatest:
42, 68, 69, 70, 72, 75, 75, 76, 80, 81, 83
Now we can see that the smallest value in this set is 42, and the highest speed is 83. The range is the largest value minus the smallest value:
Range = 83 – 42 = 41
However, you may have noticed that the speed of 42 was much slower than the rest of the speeds recorded. Therefore, 42 is considered an outlier.
In many cases, the outliers of a data set are discarded so that the range provides a more accurate picture of the data distribution. If the speed of 42 is ignored, then the range of the data set (without that outlier) is 83 – 68 = 15.
And that’s some basic info about the Probability, Statistics, and Discrete Mathematics subarea.