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2-3(cont)_changing_units

2-3(cont)_changing_units - 2.3(cont Changing Units of...

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2.3 (cont.) Changing Units of Measurement How shifting and rescaling data affect data summaries
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Shifting and rescaling: linear transformations Original data x 1 , x 2 , . . . x n Linear transformation: x *  = a + bx, (intercept a, slope b) x x * 0 a Shifts data by a Changes scale
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Linear Transformations x* = a+ b x Examples: Changing 1. from feet (x) to inches (x*):  x*=12x 2. from dollars (x) to cents (x*):  x*=100x 3. from degrees celsius (x) to degrees  fahrenheit (x*):  x* = 32 + (9/5)x   4. from ACT (x) to SAT (x*):  x*=150+40x 5. from inches (x) to centimeters (x*): x* = 2.54x 0 12 0 100 32 9/5 150 40 0 2.54
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Shifting data only: b = 1 x* = a + x Adding the same value  a  to each value in  the data set: changes the mean, median, Q 1  and Q 3  by  a   The standard deviation, IQR and variance are  NOT CHANGED Everything shifts together. Spread of the items does not change.
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Shifting data only: b = 1 x* = a + x (cont.) weights of 80 men age 19 to 24  of average height (5'8" to 5'10")   x = 82.36 kg NIH recommends maximum healthy  weight of 74 kg.  To compare their  weights to the recommended  maximum, subtract 74 kg from each  weight; x* = x – 74 (a=-74, b=1) x* = x – 74 = 8.36 kg 1. No change in shape 2. No change in spread 3. Shift by 74
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