Question at position 46 If 30 is added to every number on a list, the only one of the following that is not changed isThe medianThe meanThe standard deviationThe 75th percentileThe mode

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BlackTom AI · Accepted Answer

We are given a list of numbers and told that 30 is added to every number. We need to consider how each statistical measure responds to adding the same constant to all data points.
Option 1: The median — Adding a constant to every value shifts the entire data set by that amount, so the middle value also increases by 30. Therefore, the median changes.
Option 2: The mean — The mean sums all values and divides by the count; since every value increases by 30, the total sum increases by 30 times the number of observations, so the mean increases by 30 as well, meaning it changes.
Option 3: The standard deviation — This statistic measures the spread or dispersion of the data, not the location. Adding the same constant to every data point does not change the differences between values, so the dispersion remains the same and the standard deviation is unchanged.
Option 4: The 75th percentile — Like the median, percentiles are positional measures that move with the data. Adding 30 to all values shifts the 75th percentile upward by 30, so it changes.
Option 5: The mode — The mode is the most frequent value. If a constant is added to every entry, the most frequent value also increases by 30, so the mode changes as well.
In summary, every measure that relies on location (median, mean, 75th percentile, mode) shifts by the added constant, whereas the standard deviation, which captures spread, remains the same. This is why the standard deviation is unaffected by the uniform addition of 30 to all data points.

Question at position 46 If 30 is added to every number on a list, the only one of the following that is not changed isThe medianThe meanThe standard deviationThe 75th percentileThe mode

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