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# Math Lesson 3: Displaying Data Graphically - page 4 / 11

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order. It is the value that divides the data in half. That is, half of the data entries are less than the median, and half are greater than the median. The median is often a better measure of “average” or “center” than the mean because it is determined by its position when all the data are arranged in numerical order, and it is not affected by extreme values in the data set.

# The way to compute the median is as follows:

• 1.

Arrange all the data in order, from smallest to largest.

• 2.

If the number of data entries is odd, the median is the data value exactly in the middle, with the same number of data observations below the median as above the median.

3.

If the number of data entries is even, take the two middle values and find their average. In other words, add them together and divide their sum by 2. The result is the median. NOTE: when there is an even number of data entries, the median of a data set may not necessarily be one of the data entries.

# Practice problems:

• 2.

a) What is the median score for Mr. Sneed’s math class in Practice Problem #1 above? [80.5]

• b)

What is the median exam score for Mrs. Short’s class? [77] Now

whose class do you think did better? Why do you think we got different results when we calculated the means and the medians? What scores might have had a big influence on the mean but not the median?

c) Now let’s discover an easy way to find the median on our calculators. Under EDIT, press SortA to sort the data in List 2 in ascending order. Do the same for Mrs. Sneed’s scores in List 3. Since these are relatively small data sets, you can count to the middle value to find the median. That is easy to do for Mrs. Short’s class since there are an odd number (13) of students. For Mr. Sneed’s class, find the average of the two middle scores.

d) Carlos, the smartest student in Mr. Sneed’s class, missed the midterm exam because he was taking his driver’s test that day. When he came back, he took the test and scored 100. By adding Carlos’ score to the others in the class, how did the mean change? [It changed from 73.9 to 75.9] How did the median change? [It changed from 80.5 to 81, not much at all.]

e) What if Mr. Sneed allowed Carlos to tutor some of the students and let them retake their final exam. When they did, interestingly enough,

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