The mean is the mathematical average. The median is the middle value. The mode is the most repeated value
Mean: The new value does not affect the mean Median: The new value decreases the median by 0.1 miles Mode: The new value changes the mode to 4.0 miles and 4.3 miles Explanation: See solution.
Practice makes perfect
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 mean distance is 4 miles, the median is 4.2 miles, and the mode is 4.3 miles. Given that we run 4.0 miles on Day 11, we are asked how this additional value affects the given measures of center. Let's first add the new value to the data set.
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.
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 even number 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.
