Download Mean, Median, and Mode

Mean, Median, and Mode
Teacher
Mean, Median, and Mode
Data analysis and probability.
Students will understand how to formulate questions, analyze data, and determine probabilities.
D.1: Formulate questions that can be addressed with data and collect, organize, and display relevant
data to answer them.
7.D.1.3 Use measures of central tendency and spread to describe a set of data.
7.D.1.4 Choose between median and mode to describe a set of data and justify the choice for a
particular situation.
D.2: Select and use appropriate statistical methods to analyze data.
7.D.2.1 Choose and justify appropriate measures of central tendencies (e.g., mean, median, mode,
range) to describe given or derived data.
Vocab
Mean- (Arithmetic average) add up the numbers and divide by how many there are.
Example: (80 + 90 + 90 + 100 + 85 + 90) / 6 = 89 1/6
Median- (the number in the middle) MUST put the values in order from least to greatest,
then find the number exactly in the middle. Sometimes the answer will be a number not
in the set.
Example: 80 85 86 90 90 100
^
Since there is an even number of values he median is either in between these two
numbers, or in this case it is 88
Example: 2, 4, 5, 6, 7
There are five numbers in the set above. The median number is 5. There are two
numbers above the five and two below.
Mode- Value that occurs most often. There can be more than one mode in a set. If there is
not a number seen most often then the answer is “NO MODE” make sure the students do
not put down “0” or “nothing” for an answer.
Example: 2,2,3,3,3,3,4,5,5,6
3 occurs four times, so it is the mode of the set.
Range- difference between the lowest and highest values
Example: 10, 15, 20, 20, 34, 55, 62 88, 90
90-10; range = 80
Tips: When doing these kinds of problems, have students put the set of numbers in order
from least to greatest first. This will help them to recognize the median, mode, and solve
the range easier. If the students are required to find the mean (average) then they add all
of the numbers then divide by the amount of numbers.
Teacher
Example: Find the mode, median, range, and mean for this set of numbers: 3, 6, 9, 14, 3
First arrange the numbers from least to greatest: 3, 3, 6, 9, 14
Mode (number seen most often) = 3
3, 3, 6, 9, 14
Median (number exactly in the middle) = 6
3, 3, 6, 9, 14
Range (difference between largest and smallest numbers) = 11
3, 3, 6, 9, 14 (14 – 3 = 11)
Mean (add up all the numbers then divide by the amount of numbers) = 7
3 + 3 + 6 + 9 + 14 = 35 35 / 5 = 7
Example: Find mode, median, range, and mean of this set of number. 1, 8, 23, 7, 2, 5
First arrange the numbers from least to greatest:
1, 2, 5, 7, 8, 23
Mode = no mode
Median = 6
(5 + 7 = 12 ; 12 / 2 = 6)
Range = 22
( 23 – 1 = 22)
Mean = 7 4/6 ( 1 + 2 + 5 + 7 + 8 + 23 = 46 ; 46 / 6 = 7 4/6 or 7 2/3. This answer may
also be stated in decimals.)
Student
Practice
3. A student receives seven math scores. The median of these scores is 86 and the
range of the set of scores is 20. With these central tendencies, make a list of seven
possible test scores for this student.
4. House prices in a Santa Fe neighborhood are as follows: $155,000, $217,000,
$186,900, $138,000 and $162,000. What is the range of prices for this Santa Fe
neighborhood?
Student Answers
Students will need to calculate the total number of minutes Sina wants to exercise. 7 x 45
= 315 total minutes for the week. Next, students need to compute how many minutes she
has already exercised. 35+40+37+42+45+50=249 minutes. 315-249=66 minutes needed
to exercise on the 7th day.
If students arrange the scores from least to greatest,
137,149, 155, 158, 160, 160, 180, they will see 160 occurs most.
3. A student receives seven math scores. The median of these scores is 86 and the
range of the set of scores is 20. With these central tendencies, make a list of seven
possible test scores for this student.
There will be many correct answers for this question. Students need to understand
that the central tendencies have to be in place and then all other numbers can be
variable. First, the median (middle number) is 86 and there are seven total scores. The
85 has to be in the middle with three numbers above and three below.
____
____
____ 86 ____ ____ ____
The range is 20 so the great number minus the least number can only be 20. The
student can choose what ever the greatest and least numbers are, as long as the 85
remains in the middle.
70
____
____ 86 ____ ____ 90
The range is 20 and the median is 86, so the central tendencies have been met and the
student can fill in any other numbers that fit in the blanks.
70, 79, 82, 86, 88, 90, 90 is an example of a correct answer.
4. House prices in a Santa Fe neighborhood are as follows: $155,000, $217,000,
$186,900, $138,000 and $162,000. What is the range of prices for this Santa Fe
neighborhood?
Order the prices from least to greatest:
138,000; 155,000; 162,000; 186,900; 217,000
The range is 217,000-138,000=$79,000
Students will need to recognize they
have been asked for the most common number
which is the mode-H.