Finding the Median of a Set of Numbers
Learning Outcomes
- Find the median of a set of numbers
When Ann, Bianca, Dora, Eve, and Francine sing together on stage, they line up in order of their heights. Their heights, in inches, are shown in the table below.
Ann |
Bianca |
Dora |
Eve |
Francine |
59 |
60 |
65 |
68 |
70 |
Dora is in the middle of the group. Her height, 65", is the median of the girls’ heights. Half of the heights are less than or equal to Dora’s height, and half are greater than or equal. The median is the middle value.
Median
The median of a set of data values is the middle value.
- Half the data values are less than or equal to the median.
- Half the data values are greater than or equal to the median.
What if Carmen, the pianist, joins the singing group on stage? Carmen is 62 inches tall, so she fits in the height order between Bianca and Dora. Now the data set looks like this:
59,60,62,65,68,70
There is no single middle value. The heights of the six girls can be divided into two equal parts.
Statisticians have agreed that in cases like this the median is the mean of the two values closest to the middle. So the median is the mean of 62 and 65,262+65. The median height is 63.5 inches.
Notice that when the number of girls was 5, the median was the third height, but when the number of girls was 6, the median was the mean of the third and fourth heights. In general, when the number of values is odd, the median will be the one value in the middle, but when the number is even, the median is the mean of the two middle values.
Find the median of a set of numbers.
- List the numbers from smallest to largest.
- Count how many numbers are in the set. Call this n.
- Is n odd or even?
- If n is an odd number, the median is the middle value.
- If n is an even number, the median is the mean of the two middle values.
example
Find the median of
12,13,19,9,11,15,and 18.
Solution
List the numbers in order from smallest to largest. |
9,11,12,13,15,18,19 |
Count how many numbers are in the set. Call this n . |
n=7 |
Is n odd or even? |
odd |
The median is the middle value. |
 |
The middle is the number in the 4th position. |
So the median of the data is 13. |
try it
[ohm_question]146418[/ohm_question]
example
Kristen received the following scores on her weekly math quizzes:
83,79,85,86,92,100,76,90,88,and 64. Find her median score.
Answer:
Solution
Find the median of 83,79,85,86,92,100,76,90,88, and 64. |
|
List the numbers in order from smallest to largest. |
64,76,79,83,85,86,88,90,92,100 |
Count the number of data values in the set. Call this n. |
n=10 |
Is n odd or even? |
even |
The median is the mean of the two middle values, the 5th and 6th numbers. |
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Find the mean of 85 and 86. |
mean=285+86 |
|
mean=85.5 |
|
Kristen's median score is 85.5. |
try it
[ohm_question]146419[/ohm_question]
The next video shows another example of how to find hte median of a set of numbers.
https://youtu.be/CbKqFc-EPDsLicenses & Attributions
CC licensed content, Original
CC licensed content, Shared previously
- Ex: Find the Median of a Data Set. Authored by: James Sousa (Mathispower4u.com). License: CC BY: Attribution.
CC licensed content, Specific attribution
- Prealgebra. Provided by: OpenStax License: CC BY: Attribution. License terms: Download for free at http://cnx.org/contents/caa57dab-41c7-455e-bd6f-f443cda5519c@9.757.