Question

X X-µ
69 -9.5
72 -6.5
74 -4.5
76 -2.5
79 0.5
80 1.5
82 3.5
83 4.5
85 6.5
85 6.5

785 0

How does this relate to the description of the mean as the center of gravity of a date set?
What value for the mean would you expect if you multiplied each score by 10?
What value for the mean would you expect if your subtracted 20 from each score?
What would happen to the median if you subtracted 40 from your lowest value?
What would happen to the mean if you subtracted 40 from your lowest value
Comment the difference between the effect on the median and effect on the mean?
If you are have the value of the mean and the number of scoresin the data set, are you able to calculate by working backwards

Answer 1

1. The information relates to the fact that the sum of deviations of all the observations from the mean is 0.

2. If each score is multiplied by 10, then the obtained mean will be 10 times more than the earlier one.

3. If we subtract 20 from each score then the obtained mean will be reduced by 20.

4. If we subtract 40 from the lowest value, then the order of the observations will not be changed. Hence, the median will not be affected.

5. If the subtract 40 from the lowest value then the mean will be reduced by 40/n, where, n is the total number of observations.

6. Median will not be changed by change in exat values as long as the order of the observations is not impacted. However, mean is affected if we change even one observation.

7. If we have the value of mean and the number of scores in the data, then we can only calculate the sum of scores by multiplying mean and number of scores.