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Shift and Scale Changes
Module 4b
Distribution Properties
• Shift Changes: adding or subtracting a
number from the each of the values.
mean
Distribution Properties
• Shift Changes: adding or subtracting a
number from the mean.
Distribution Properties
• Shift Changes: adding or subtracting a
number from the mean.
Distribution Properties
• The mean, median, Q1, Q3, maximum, and
minimum all shift when there is a shift
change. The shift change, say c, is added or
subtracted to each of the statistics
accordingly.
• The measures of spread (standard deviation,
variance, IQR, and range) do not change
when there is a shift change.
Distribution Properties
• Scale Changes: multiplying or dividing each
of the values by a number.
mean
Distribution Properties
• Scale Changes: multiplying or dividing each
of the values by a number.
Distribution Properties
• Scale Changes: multiplying or dividing each
of the values by a number.
Distribution Properties
• The mean, median, Q1, Q3, maximum, and
minimum all change when there is a scale change
unless they are zero. Each is multiplied or divided
by the scale change c.
• The measures of spread (standard deviation,
variance, IQR, and range) always change when
there is a scale change. The standard deviation,
IQR, and range are multiplied or divided by the
scale change c. The variance is multiplied or
divided by c2.
Distribution Properties
• Suppose we measure the weight of everyone on
a football team and obtain the following
statistics for a team report:
–
–
–
–
–
Mean: 230 lbs.
Std. Dev.: 50 lbs.
Variance: 2500 lbs.
Min.: 170 lbs.
Max.: 350 lbs.
Median: 240 lbs.
Q1: 200 lbs., Q3: 280 lbs.
IQR: 80 lbs
Range: 180 lbs.
Distribution Properties
• Now suppose we find that the scale was 10 lbs.
under, so we need to add 10 lbs. to every
weight. What would happen to each of the
following statistics?
Original
Mean: 230 lbs.
Median: 240 lbs.
s: 50 lbs.
Q1: 200 lbs.
Q3: 280 lbs.
After Shift Change
Distribution Properties
• Now suppose we found out the scale was 10
lbs. under so we need to add 10 lbs. to every
weight. What would happen to each of the
following statistics?
Original
Variance: 2500 lbs.
IQR: 80 lbs.
Min: 170 lbs.
Max: 350 lbs.
Range: 180 lbs.
After Shift Change
Distribution Properties
• Further, suppose we find that we are supposed to
report the weights and statistics in kilograms, not lbs
(Remember, 1 lb = 0.6 kilograms). What would
happen to each of the following statistics?
After Shift Change
Mean: 240 lbs.
Median: 250 lbs.
s: 50 lbs.
Q1: 210 lbs.
Q3: 290 lbs.
After Shift and Scale Change
Distribution Properties
• Further, suppose we found out that we are supposed to
report the weights and statistics in kilograms, not lbs
(Remember, 1 lb = 0.6 kilograms). What would
happen to each of the following statistics?
After Shift Change
Variance: 2500 lbs.
IQR: 80 lbs.
Min: 180 lbs.
Max: 360 lbs.
Range: 180 lbs.
After Shift and Scale Change
Distribution Properties
• Now our report is ready!