The mean of 10 observations is 21. If each score is divided by 3, find the new mean.
(1/10)( X1/3 + X2/3 + ...(X10/3) =
(1/30) (X1 + X2 + ....(X10)
so
new mean = (1/3) times old mean
lets take an example,
observations are 1,2and3
hence mean is= 1+2+3/3=6
when each observation is divided by 3 then
1/3+2/3+3/3/33=4/3
1/3+2/3+3/3/3=4*1/3
Hence mean become 1/3 times then old mean.
Hence in question the new mean is 21*1/3=21/3=7.
To find the new mean of the observations after each score is divided by 3, you need to divide each individual score by 3 and then calculate the mean of the new set of observations.
Given that the mean of the original 10 observations is 21, it means that the sum of the 10 scores is 21 multiplied by 10, which is equal to 210 (mean = sum of scores / number of scores).
To find the new mean, you need to divide each score by 3. This means that each original score will be divided by 3.
So, if we divide each original score by 3, the sum of the new scores will be 210 / 3.
Therefore, the sum of the new scores is 70 (210 / 3 = 70).
Since there are still 10 observations after dividing each score by 3, the new mean is calculated by dividing the sum of the new scores (70) by the number of scores (10).
Hence, the new mean of the observations after each score is divided by 3 is 7 (70 / 10 = 7).