Linear Transformations
Linear transformations: When every value of the variable x is transformed into a new value x new given
by the equation xnew  a  bx .
1. Complete each table below.
Original Data (x)
3, 6, 9, 9, 9, 10, 10
Median
Mean
Range
IQR
St. Dev.
Variance
IQR
St. Dev.
Variance
Multiply each value in the original data by 3 and complete the table.
Median
Mean
Range
IQR
xnew  3x
St. Dev.
Variance
Multiply each value in the original data by 2 and add 3 and complete the table.
Median
Mean
Range
IQR
St. Dev.
xnew  3  2 x
Variance
Add 4 to each value in the original data and complete the table.
Median
Mean
Range
xnew  4  x
2. How is each summary statistic of x affected by the linear transformation xnew  a  bx ?
Median new =
Mean new =
Range new =
IQR new =
St. Dev. new =
Variance new =
3. What is the shape of the distribution of the original data?
4. How does a linear transformation of xnew  a  bx affect the shape of the data?
5. Suppose Mr. Selvaag gave a test for which x  70 and s  21 . He wants to apply a linear
transformation xnew  a  bx to “scale” the grades so that x new  82 and s new  7 . Find a and b.