CHANGE OF ORIGIN AND SCALEQARM

SHIFT IN DATA POINTS

DISTRIBUTION PROPERTIESShift Changes: adding or subtracting a number from the each of the values.mean

DISTRIBUTION PROPERTIESShift Changes: adding or subtracting a number from the mean.

DISTRIBUTION PROPERTIESShift Changes: adding or subtracting a number from the mean.

DISTRIBUTION PROPERTIESThe 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 PROPERTIESScale Changes: multiplying or dividing each of the values by a number.mean

DISTRIBUTION PROPERTIESScale Changes: multiplying or dividing each of the values by a number.

DISTRIBUTION PROPERTIESScale Changes: multiplying or dividing each of the values by a number.

DISTRIBUTION PROPERTIESThe 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.

QUICK REVISEIf we add a constant to values, the mean will increase of this constant.If we multiply our values by a constant , the mean will be multiplied by this constant.If we add a constant to values, the dispersion of the values from the mean is not changed, so the variance is not affected and remains the same.If we multiply our values by a constant, the standard deviation is multiplied by this constant, the variance is multiplied by the square of this constant