change in the data value to give a lower/equal mean than the median

mdnr

New member
Does anyone knows, how to change (or which ONE VALUE of data do I have to change), so that the mean of this data are: 1. lower than the median, and 2. as equal as the median. For example if I have the data: 1, 1.2, 1.4, 1.6, 1.6, 1.8, 2.0, 2.6, 2.8, 2.8, 3.
I've read some on the internet which says that:
median + (new value - old value)/number of value (or we called n)= mean

then I've tried to make a new mean value which is lower than the old mean. But it's always give a negative result for the ONE NEW VALUE (of the data). Is it true? So I can't have any ONE NEW POSITIVE VALUE (to make the mean lower/equal than the median)?

ksdhart2

Senior Member
Realistically, you can change any one of the values to alter the mean and median. Which one might be best to change and what to change it to depends on exactly what you want to change the mean and median to. The problem you posted says that for part(a), you need to change one value so that the mean is less than the median, and for part (b) you need to change one value so the mean and the median are equal. Surely you've noticed, just by process of experimentation, that changing any of the values changes both the median and the mean. Why is that?

Now, if I'm understanding your question correctly, you're asking why you have to lower one value in order to lower the mean. Well, to see why that is, maybe try it the other way around - what happens if replace one value with a larger value? Does the mean increase, decrease, or stay the same? Why? What happens to the median? Does it increase, decrease, or stay the same? Why? Now what happens if you replace one value with a smaller value. Try answering the same questions for that case. How does this all help you solve the problem at hand?