Consider the given table.
| Miles Run
|
| 3.5
|
4.1
|
| 4.0
|
4.3
|
| 4.4
|
4.5
|
| 3.9
|
2.0
|
| 4.3
|
5.0
|
The above shows the number of miles we ran each day for
10 days. The distance is
4 miles, the is
4.2 miles, and the is
4.3 miles. Given that we run
4.0 miles on Day
11, we are asked how this additional value affects the given . Let's first add the new value to the .
3.5,4.0,4.4,3.9,4.3,4.1,4.3,4.5,2.0,5.0,4.0
Now we can analyze each measure one at a time. Let's do it!
Mean
The mean of a numerical data set is the sum of the data divided by the number of data values. After the new value is added, we have
11 data values. Then we will divide the sum of the data by
11.
xˉ=Number of ValuesSum of Values
xˉ=113.5+4.0+4.4+3.9+4.3+4.1+4.3+4.5+2.0+5.0+4.0
xˉ=4
We can see that the new value does not affect the mean.
Median
The median of a numerical data set is the middle number when the values are written in numerical order. If the data set has an of values, the mean of the two middle values will be the median. Let's write the data in numerical order.
2.0,3.5,3.9,4.0,4.0,4.1,4.3,4.3,4.4,4.5,5.0
In this case, the median is
4.1 miles. Comparing it with the original median
4.2, we can see that the new value decreases the median by
0.1 miles.
Mode
The mode of a data set is the value or values that occur most often. Let's take a look at our data.
2.0,3.5,3.9,4.0,4.0,4.1,4.3,4.3,4.4,4.5,5.0
In this case, we can see the mode changes to
4.0 miles and
4.3 miles rather than only being
4.3 miles as in the previous
10 days.
