Question

Suppose you have a data set and the mean, median and the standard deviation are 10, 10 and 2, respectively. Someone multiplies all your data points by 3. Call these data the new data.

The mean of the new data will be _______________________

The Median of the new data will be _______________________

The standard deviation of the new will be _______________________

The variance of the new will be _______________________––

Answer 1

Answer 2

When all data points in a dataset are multiplied by a constant, such as 3 in this case, the following transformations occur:

1. Mean: The mean of the new data will also be multiplied by the same constant. Therefore, the mean of the new data will be 3 times the original mean. Mean of the new data = 3 * 10 = 30

2. Median: The median of the new data will remain unchanged. Multiplying all data points by a constant does not affect the relative ordering of the values, so the median remains the same. Median of the new data = 10

3. Standard Deviation: The standard deviation of the new data will also be multiplied by the absolute value of the constant. In this case, the constant is 3, so the standard deviation of the new data will be 3 times the original standard deviation. Standard deviation of the new data = 3 * 2 = 6

4. Variance: The variance of the new data will be equal to the square of the standard deviation of the new data. Variance of the new data = (Standard deviation of the new data)^2 = 6^2 = 36

Therefore, the mean of the new data will be 30, the median will be 10, the standard deviation will be 6, and the variance will be 36.