15.1. Mean, Median and Mode http://www.ck12.org
the middle number after the data has been ordered. When the data has an even number of counts, the median is the
average of the two most central numbers.
Themodeis the most often occurring number in the data. If there are two or more numbers which occur equally
frequently, then the data is said to bebimodalormultimodal.
Withdescriptive statistics, your goal is to describe the data that you find in a sample or is given in a problem.
Withinference statistics, your goal is use the data in a sample to draw conclusions about a larger population.
Guided Practice
- Ross is with his friends and they want to play basketball. They decide to choose teams based on the number of
cousins everyone has. One team will be the team with fewer cousins and the other team will be the team with more
cousins. Should they use the mean, median or mode to compute the cutoff number that will separate the two teams? - Compute the mean, median, and mode for the following numbers.
1, 4, 5, 7, 6, 8, 0, 3, 2, 2, 3, 4, 6, 5, 7, 8, 9, 0, 6, 5, 3, 1, 2, 4, 5, 6, 7, 8, 8, 8, 4, 3, 2 - The cost of fresh blueberries at different times of the year are:
$2.50, $2.99, $3.20, $3.99, $4.99
If you bought blueberries regularly what would you typically pay?
Answers: - Ross and his friends should use the median number of cousins as the cutoff number because this will allow each
team to have the same number of players. If there are an odd number of people playing, then the extra person will
just join either team or switch in later. - The mean is 4.6061. The median is 5. The mode is 8.
- The word “typically” is used instead of average to allow you to make your own choice as to whether mean,
median, or mode would make the most sense. In this case, mean does make the most sense. The average cost is
$3.53.
Practice
You surveyed the students in your English class to find out how many siblings each student had. Here are your
results:
0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 10, 12
- Find the mean, median, and mode of this data.
- Why does it make sense that the mean number of siblings is greater than the median number of siblings?
- Which measure of central tendency do you think is best for describing the typical number of siblings?
- So far in math you have taken 10 quizzes this semester. The mean of the scores is 88.5. What is the sum of the
scores? - Findxif 5, 9, 11, 12, 13, 14, 16, andxhave a mean of 12.
- Meera drove an average of 22 miles a day last week. How many miles did she drive last week?
- Findxif 2, 6, 9, 8, 4, 5, 8, 1, 4, andxhave a median of 5.
Calculate the mean, median, and mode for each set of numbers: - 11, 15, 19, 12, 21, 34, 15, 28, 24, 15, 27, 19, 20, 13, 15