If every value in the data set is increased by a constant k, the mean, median, and mode of the new data set can be found by adding k to each of the original statistics.
Mean: 8 Median: 7 Mode: 5
Practice makes perfect
Consider the given data set.
3 , 5 , 1 , 5 , 1 , 1 , 2 , 3 , 15
We want to find the mean, median, and mode of data set obtained by adding the given constant, k= 4, to each value.
If every value in the data set is increased by the constant 4, then the statistics of the new data set will behave in a consistent, predictable way.
The new mean, median, and mode can be found by adding 4 to the mean, median, and mode of the original data set.
The range and standard deviation will not change.
Notice that only the measures of center are increased by the constant and the measures of spread will not change. This is because the distances between the individual values do not change.
To begin, let's find the statistics of the original data set.
Mean
The mean of a data set x is calculated by finding the sum of all of the values in the set and then dividing by the number of values. In this case, there are 9 values in the set.
When the data are arranged in numerical order, the median is the middle value — or the mean of the two middle values. Let's arrange the given values and find the median.
1 , 1 , 1 , 2 , 3 , 3 , 5 , 5 , 15
The median of this set is 3.
Mode
The mode is the value or values that appear most often in a set of data.
Let's find the mode of the given values.
3 , 5 , 1 , 5 , 1 , 1 , 2 , 3 , 15
The value that appears most often is 1, so this is our mode.
Adding a Constant
Finally, we can find new values of the statistics by adding 4 to the mean, median, and mode.
