Besides matrices, another way to organize data is by using statistics. Statistics help describe situations that are not exact. You see them every time you pick up a newspaper. Businesses use them in quality control and to find out which items to market. The following are some examples:
A sample of voters shows that 40% currently approve of the president’s policies.
When asked to try the two brands, 75% of the shoppers liked our cola.
Karen works in quality control in a metal works plant; today she found that 4% of the parts she tested were defective.
A medical researcher has found that a new medication reduces pain in about 65% of the patients tested.
There are countless examples in of statistics in business, politics, education, medicine, and every walk of life.
You have already used some of the methods for dealing with data in the first part of this course: bar graphs, circle graphs, line graphs, stem and leaf plots. You also learned about measures of central tendency: mean, median, and mode. In this section, you will look at two other ways to organize data: histograms and box plots.
First, let’s review the measures of central tendency. They were give this name because they are each a way to measure the central point of a group of numbers.
Measures of Central Tendency
Mean (average) – The sum of a group of numbers divided by the number of addends.
Median – The middle number, when a group is arranged in order from least to greatest. If there are two middle numbers, average them.
Mode – The number that occurs most frequently in a list of numbers.
Example 1: Finding the Mean, Median, and Mode
A basketball team had these scores in the nine games they had played so far:
64, 100, 92, 64, 86, 65, 90, 77, 89.
Find the mean, median and mode for the team.
Find the mean by adding and dividing by nine, since there are nine numbers.
(64 + 100 + 92 + 64 + 86 + 65 + 90 + 77 + 89) / 9 = 727 / 9 = 80.777…≈ 80.8
The mean score for the team is about 81 points.
To find the median, order the scores from least to greatest and find the middle number.
In order, they are 64, 64, 65, 77, 86, 89, 90, 92, and 100.
There are nine numbers, so the fifth one is the middle.
The median is 86.
The mode is the number that appears the most often. The mode for this set is 64.
Think About It
In the example above, the measures of central tendency gave three very different answers. Which of the answers is the best measure for the “center” in this case?
When you examine the numbers in order, it seems obvious that the central scores are in the 80’s. So, the mode would not be near the center in this case.
Next, notice that there are three scores very close to each other in the 60s. It would be fair to say that these three numbers might artificially lower the mean as a central indicator. Therefore, the median of 86 would be the better central indicator.
Practice
Find the mean, median, and mode of each set of data. Round decimals to the nearest hundredth.
Measures of Central Tendency 
Think About It
Practice
