Question

In: Statistics and Probability

Suppose you calculated the mean, median, mode, and sample standard deviation of a data set. The...

Suppose you calculated the mean, median, mode, and sample standard deviation of a data set. The results are shown below.

Mean: 44
Median: 31
Mode: 46
Sample Standard Deviation: 2

If each number in the data set was decreased by 4 units, what would be the new values of these statistics?

Fill in your results below.

New Mean:

New Median:

New Mode:

New Sample Standard Deviation:

Expert Solution

Given:

Mean = 44 , Median = 31, Mode = 46, Sample standard deviation = 2

Mean = sum of all observation / Total number of observation.

If every observation is decrease by 4 , mean will be decrease by 4

New mean is 44-4 = 40

New mean is 40

Median: If we arrange data in ascending or descending order, middle value of the data is median.

If all values decrease by 4 , median value will be decrease by 4.

New median = 27

Mode = Value that having maximum frequency.

Mode will be decrease by 4.

New mode: 42

Sample standard deviation =

Even if each value is decrease by 4, deviation from each value will remains same.

There is no effect on sample standard deviation.

New sample standard deviation = 2

Please refer this sample data. We get mean . median, mode and standard deviation.

Subtract 4 by each value, we will get new sample data. Find mean . median, mode and standard deviation and compare with original data.

You can observe mean . median, mode decreased by 4, while standard deviation will remains same.

orchestra answered 2 years ago

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