Effects of Scaling on Statistics

The video tutorial explains how adding or subtracting a constant from a data set affects the mean, median, and mode but not the range or standard deviation. Conversely, multiplying a data set by a scale factor affects all statistical values, including the range and standard deviation. Examples are provided to illustrate these concepts, showing how adding a point shifts the data without changing dispersion, while scaling alters all values proportionally.

What happens to the mean when a constant is added to each data point in a dataset?

• It decreases by the constant.

• It remains unchanged.

• It increases by the constant.

• It is multiplied by the constant.

Which statistical measure is unaffected by adding a constant to each data point?

• Range

• Mode

• Median

• Mean

When a dataset is multiplied by a scale factor, what happens to the standard deviation?

• It is divided by the scale factor.

• It is multiplied by the scale factor.

• It is subtracted by the scale factor.

• It remains the same.

In the example dataset, what is the mean of the scores 6, 7, 8, 9, and 10?

• 9

• 8

• 7

• 10

What is the range of the dataset 6, 7, 8, 9, and 10?

• 3

• 5

• 2

• 4

How is the standard deviation calculated in the example dataset?

• By multiplying all data points by a constant.

• By squaring the deviations from the mean, averaging them, and taking the square root.

• By finding the difference between the maximum and minimum values.

• By adding all data points and dividing by the number of points.

What happens to the median when a constant is added to each data point?

• It decreases by the constant.

• It remains unchanged.

• It increases by the constant.

• It is multiplied by the constant.

After adding 1 to each score in the dataset, what is the new mean?

• 8

• 10

• 7

• 9

What remains unchanged when a constant is added to each data point?

• Standard Deviation

• Mean

• Median

• Mode

What happens to the mode when a constant is added to each data point?

• It is multiplied by the constant.

• It decreases by the constant.

• It remains unchanged.

• It increases by the constant.