If every value in the data set is multiplied by a constant k>0, the mean, median, and mode of the new data set can be found by multiplying each of the original statistics by k.
Mean: 15.12 Median: 14.4 Mode: Does not exist
Practice makes perfect
Consider the given data set.
12 , 9 , 17 , 15 , 10
We want to find the mean, median, and mode of a data set obtained by increasing each value by 20 %. To increase by 20 % means to multiply by 1.2. If every value in the data set is multiplied by the constant 1.2, the mean, median, and mode of the new data set can be found by multiplying each original statistic by 1.2.
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 the set. In this case, there are 5 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.
9 , 10 , 12 , 15 , 17
The median of this set is 12.
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.
12 , 9 , 17 , 15 , 10
Since the data set does not contain any repeated values, there is no mode.
Multiplying by a Constant
Finally, we can find the new values of the statistics by multiplying each value by 1.2.
