![]() The size of the quartiles may be different, but the number of data points in each quartile is the same. The box-and-whisker plot essentially divides the data set into four sections (or quartiles): whisker, box, box, whisker. One stretches from 3 (the least value in the set) to 6, and the other goes from 15 to 20 (the greatest value in the set). The “whiskers” are the line segments on either end. Notice that one “box” (rectangle section) begins at 6 (the median of the lower set) and goes to 11 (the median of the full set), and the other box goes from 11 to 15 (the median of the upper set). Do you see any similarities between the numbers above and the location of the box? So, the median of the set is 11, the median of the lower half is 6, and the median of the upper half is 15.ģ, 5, 5, 6, 7, 9, 10, 11, 11, 12, 12, 15, 18, 18, 20Ī box-and-whisker plot for this data set is shown here. A box-and-whisker plot requires you to find the median of these numbers as well! This data set has 15 numbers, so the median will be the 8th number in the set: 11.įinding the median of the data set essentially divides it into two-a set of numbers below the median, and a set of numbers above the median. Here is a sample set of 15 numbers to get us started.ġ2, 5, 18, 20, 11, 9, 3, 5, 7, 18, 12, 15, 6, 10, 11Ĭreating a box-and-whisker plot from this data requires finding the median of the set. These graphs provide a visual way of understanding both the range and the middle of a data set. Iii) Half the high temperatures were above 91º and half were below 91º.Īnother type of graph that you might see is called a box-and-whisker plot. Ii) The high temperature was never lower than 92º. I) The high temperature was exactly 91º on each of the seven days. Which of the following are true statements? If this data represented the ages of students on a chess team, for example, you would have a good idea that everyone on the team was about 11 years old, with a few older and younger members.ĭuring a seven-day period in July, a meteorologist recorded that the median daily high temperature was 91º. This shows some consistency in the data, with a middle (average) value of about 11. In this case, the mean, median, and mode are very close in value. The number 11 appears most often, 3 times. To find the mode, look for the number that appears most often. Since there are 10 numbers (an even number) the median is the mean of the middle two numbers (the 5 th and 6 th), or halfway between 11 and 12. To find the median, first order the numbers from least to greatest. ![]() To find the mean, add together all the numbers and divide that sum by the number of numbers. In the case of test taking, the mode is often meaningless-unless there are a lot of 0s, which could mean that the student didn’t do his homework, or really doesn’t know what’s going on!įind the mean, median, and mode of the following set of numbers: Notice, also, that there is no mode, since Carlos did not score the same on two tests. That’s all you are really after when using median and mean-finding the center, or middle, of the data. Looking at these measures, you notice that the middle of the data set is in the mid-80s: the mean value is 86, and the median value is 84. What can be learned from the mean, median, and mode of Carlos’ test scores? Notice that these values are not the same.īoth the mean and the median give us a picture of how Carlos is doing. Since each number appears exactly one time, there is no mode. There are five scores, so the middle test score is the third in the ordered list. To find the median, order the test scores from least to greatest. To find the mean, add all the tests scores together and divide by the number of tests. Find the mean, median, and mode of his scores. Look at the example that follows-the mean is 18, although 18 is not in the data set at all.Ĭarlos received the following scores on his mathematics exams: 84, 92, 74, 98, and 82. In the previous data set, notice that the mean was 4 and that the set also contained a value of 4. Then, divide this sum by the number of numbers in the set, which is 6. For example, if you are asked to find the mean of the numbers 2, 5, 3, 4, 5, and 5, first find the sum: 2 + 5 + 3 + 4 + 5 + 5 = 24. Knowing the process helps when you need to find the mean of more than two numbers. A mathematical way to solve this, though, is to add 10 and 16 (which gives you 26) and then divide by 2 (since there are 2 numbers in the data set). What number lies half way between them? 13. You can often find the average of two familiar numbers, such as 10 and 16, in your head without much calculation. Also referred to as the “arithmetic mean,” it is found by adding together all the data values in a set and dividing that sum by the number of data items. “Mean” is a mathematical term for “average” which you may already know.
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