The distribution of raw scores on a particular achievement test has a mean of 500500500 and a standard deviation of 808080. If each score is increased by 252525, what will be the mean and standard deviation of the distribution of new scores?

Accepted Solution

Answer:Mean will increase by 25 i.e. it will become 75.And, Standard deviation will remain same i.e. 80.Step-by-step explanation:Since, Each score is increased by 25. So, the Mean will increase by 25 i.e. it will become 75. Example: Mean of {4, 5, 6, 7, 8} = 6and if every observation will increase by 2 then Mean of {6, 7, 8, 9, 10} = 8.Thus, the Mean will also increase by 2.Also, Standard deviation measures the dispersion(scatter) of data and it is the distance from the mean. Since there is no change in distance. Thus there will be no change in standard deviation.Further, Mean is used to measure the central tendency of data which represents the whole data in the best way. It can be found as the ratio of the sum of all the observations to the total number of observations. Standard Deviation is the square root of the sum of square of the distance of an observation from the mean.