Summer Mathematics Packet
IM Page 11
Mean, Median, and Mode
Hints/Guide:
We need to define some terms to solve problems involving mean, median, and mode. Mean is
the sum of the numbers being considered divided by the total number of numbers being
considered (also called "average"). Median is the number in the middle of the data set after the
numbers have been placed in order from least to greatest. If there is an even number of elements,
the median is the mean of the two numbers in the middle of the data set. The mode is the
number or numbers that occur most frequently in a data set. For example, with the data set of 56,
62, 67, 45, 81, 76:
Mean is 56 + 62 + 67 + 45 + 81 + 76 = 387 and 387 ÷ 6 = 64.5, so the mean is 64.5
Median is (in order the data is 45, 56, 62, 67, 76, 81) the mean of 62 and 67, which is (62
+ 67 = 129 and 129 ÷ 2 = 64.5) also 64.5.
There is no mode, because no number occurs more than once.
Exercises:
SHOW ALL WORK. Use a separate sheet of paper (if necessary) and staple to this page.
Find the mean, median, and mode of each of the following data sets:
1. 54, 65, 74, 35, 87 2. 54.6, 45.98, 67.4, 55.6, 45.7, 58.9
3. 122, 145, 156, 176, 198, 202 4. 11, 14, 16, 15, 32, 23, 27, 27, 23, 43
5. 6, 7, 8, 4, 6, 5, 8, 3, 6, 8, 5, 4 6. -4, 7, -3, 4, 8, 12, -5, -3, 8, 16, 9
7. 43, 56, 98, 67, 87 8. 12, 15, 14, 18, 33, 32, 24, 26, 27
9. 13.2, 17.6, 18.34, 12.54, 17.4, 15.8, 13.7, 17.6
10. Write a data set that has 5 numbers with a mean of 84 and a median of 86.