Describe the effect of adding, subtracting, multiplying by, or dividing by a constant on the shape, center, and variability of a distribution of data.
Adding and subtracting does not affect shape, only where the shape is. Multiplying keeps the shape but it is more spread out. Dividing condenses the shape. Mean and median change from adding, subtracting, multiplying, and dividing. IQR, Range, and Standard Deviation change from multiplying and dividing only.
Adding a constant to a set of data will shift the distribution to the right or left, depending on the value of the constant. The center of the distribution, such as the mean or median, will also shift by the same value as the constant. However, the range and standard deviation of the data will remain unchanged.
Subtracting a constant from a set of data will similarly shift the distribution, but in the opposite direction. The center of the distribution will also shift by the same value as the constant. Again, the range and standard deviation of the data will remain unchanged.
Multiplying a set of data by a constant will stretch or shrink the distribution. The center of the distribution will remain in the same location, but the range and standard deviation of the data will change. If the constant is greater than 1, the distribution will be stretched and become more spread out. If the constant is between 0 and 1, the distribution will be compressed and become more tightly clustered.
Dividing a set of data by a constant will have a similar effect as multiplying by a constant, but in the opposite direction. The center of the distribution will remain in the same location, but the range and standard deviation of the data will change. If the constant is greater than 1, the distribution will be compressed and become more tightly clustered. If the constant is between 0 and 1, the distribution will be stretched and become more spread out.
In summary, adding or subtracting a constant will shift the center of the distribution without affecting its variability, while multiplying or dividing by a constant will change its variability without affecting its center.
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