Consider the given information of a data set.
Mean:27 Median:32 Mode:18
Range:41 Standard Deviation:9
We are asked to find the shown measures after each value of the data set is multiplied by 3 and then increased by 8. To do so, let's apply one change at a time.
Multiplication by 3
When each value of a data set is multiplied by a real number k>0, the measures of center and variation can be found by multiplying the original measures by k. With this in mind let's find the new values of each measure shown. In this case, k=3.
Measure
Original Data Set
* 3
Data Set Multiplied by 3
Mean
27
27 * 3
81
Median
32
32 * 3
96
Mode
18
18 * 3
54
Range
41
41 * 3
123
Standard Deviation
9
9 * 3
27
Increasing by 8
When a real number k is added to each value in a data set, the measures of center of the new data set can be found by adding k to the original measures of center. Additionally, the measures of variation are the same. Applying this information to the last column of the above table, we can find the measures of the data set multiplied by 3 and then increased by 8.
Measure
Data set Multiplied by 3
+ 8
(Data set * 3) + 8
Mean
81
81 + 8
89
Median
96
96 + 8
104
Mode
54
54 + 8
62
Range
123
-
123
Standard Deviation
27
-
27
Conclusion
The last column of the above table represents the measures of the data set after being multiplied by 3 and increased by 8.
Mean:89 Median:104 Mode:62
Range:123 Standard Deviation:27
