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Lesson 2.3 Mean, Median and Mode
Mean
The mean is the same as the average. To find the mean, add all the values and divide by the total number of values.
Example: {2, 3, 5, 6}
The mean 
The letter x with a bar over it,  , represents the sample mean.
The Greek letter, µ , represents the population mean.
Median
The median is the middle value of a set of numbers that has been ordered from smallest to largest. The upper case letter M is used for the median.
Example: A sample of statistics exam scores for 14 students are (in order from smallest to largest) as follows:
53, 59, 63, 63, 72, 72, 76, 78, 81, 83, 84, 84, 90, 93
Notice that 14 is an even number.
The median is between 7th and 8th values (the middle two values). The 7th value is 76 and the 8th value is 78. The median M =
Example: A second sample of statistics exam scores for 15 students are (in order from smallest to largest) as follows:
52, 60, 65, 67, 70, 71, 74, 76, 78, 78, 78, 80, 86, 89, 95
Notice that 15 is an odd number.
The median is the 8th value (the middle value). The 8th value is 76 so the median M = 76.
Mode
The mode is the most frequent value in the set of numbers.
Example: In the data set
52, 60, 65, 67, 70, 71, 74, 76, 78, 78, 78, 80, 86, 89, 95, the most frequent value is 78. The mode = 78.
Example: In the data set
52, 53, 53, 53, 60, 67, 72,72,72, 90, both 53 and 72 occur the most number of times (3 times each) so there are two modes, 53 and 72. We call this set of data bimodal meaning it has two modes.
Think About It
Which is the "best" measure of the center of a set of data? That all depends on the data. If the data tend toward being different values with no extremely large or small values, the mean might be the best measure of the data. If the data is highly skewed, the median might be the best measure of the center. If the data repeats values, the mode might be the best measure.
Example: A shoe store sells women's shoes in sizes 5 through 11. The average shoe size is 7 1/2, the median size is 8 1/2, and most frequent shoe size is 8. Which is the best measure?
Because the most frequent shoe size is 8, the manager orders more shoes in size 8 than any other size. Even though the average shoe size is 7 1/2 and the median is 8 1/2, the mode is the best measure of the center for this particular shoe store.
Example: Suppose in a community of 7 households, the yearly income is (in dollars)
50,000
53,000
58,000
59,000
60,000
61,000
5,000,000
The mean is $763,000 and the median is $59,000. Which is the best measure?
The median better represents the center of income of the majority of households. In this case, the median is the better measure of the center of the data.
TI-83 Example Showing the Mean, the Median, and the Quartiles
Example
The TI-83 easily calculates the mean, the median, and the quartiles. Please close the window when you are finished viewing the example. You will return here.
Please continue to the next section of this lesson.
Up » 2.1 Graph » 2.2 Quartiles and Percentiles » 2.3 Mean, Median and Mode » 2.4 Variance and Standard Deviation
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