Finding the Median
Wednesday, January 31st, 2007Sometimes the median can be confused with the average. In statics the median is where the typical person falls. We don’t say average because when averaging, the average is often skewed because any large numbers used will pull the average away from where the middle person actually is. For example:
Raw Data
| 0 - 5 | 5, 3, 2, 3, 4, 3, 5 |
| 6 - 10 | 6, 6, 6, 9, 8, 7, 6, 7, 9, 6, 10, 7, 8, 9, 6, 6, 7, 7, 8 |
| 11 - 15 | 11, 12, 13, 14, 14, 13 |
| 16 - 20 | 16, 17, 17 |
| 21+ | 23 |
Distributed Data
The next step is to figure out how many people fit in each category.
| Number of Miles Driven | # of People | % |
| 0 - 5 | 7 | 19% |
| 6 - 10 | 19 | 53% |
| 11 - 15 | 6 | 17% |
| 16 - 20 | 3 | 8% |
| 21 + | 1 | 3% |
| Total | 36 | 100% |
Finding the Middle Person
The equation to find the middle person is simple. All we need to do is find the total number of people, which is 36 in this case. We ad one to the total number of people and then divid that by 2.
L = ( n + 1 ) / 2
L = the lower end of the category that contains the middle person. The middle person will be 18.5.
n = total number of people, 36.
CF = total number of people in the category or categories that come before the category containing the middle person. Since 18.5 falls in the “6 - 10 miles” category this number will be 7. If there were two or more categories before this one, then we would add the number of people in each category together to get this value.
f = the number of people in the category containing the middle person. The number of people in this category is 19.
i = the interval of the range of the category that has the middle person to the category after it. For this instance the interval is 5 because 11 - 6 = 5.
Now we can type it into our graphing calculators to get:
18.5 + ( ( ( 36 / 2 ) - 7 ) / 19 ) * 5 = 21.39473684