14) A population of N = 20 scores has a mean of µ = 15. One score in the population is changed from X = 8 to X =28. What is the value for the new population mean?
(20(15) +28 -8)/20
(300+28-8)/20
320/20 = 16
To find the new population mean after changing one score from 8 to 28, we need to recalculate the mean based on the updated data.
Here are the steps to find the new mean:
1. Calculate the sum of the original scores: Sum = N * µ.
In this case, Sum = 20 * 15 = 300.
2. Subtract the original score (X = 8) from the sum: Sum - X = 300 - 8 = 292.
3. Add the new score (X = 28) to the new sum: New Sum = 292 + 28 = 320.
4. Calculate the new mean by dividing the new sum by the total number of scores: New Mean = New Sum / N.
New Mean = 320 / 20 = 16.
Therefore, the value for the new population mean is 16.
To find the new population mean after changing one score, we need to calculate the sum of all the scores in the population.
1. Start by finding the sum of the original 20 scores:
sum_original = N * µ
sum_original = 20 * 15
sum_original = 300
2. Subtract the original score that was changed:
sum_new = sum_original - X (old)
sum_new = 300 - 8
sum_new = 292
3. Add the new score:
sum_new = sum_new + X (new)
sum_new = 292 + 28
sum_new = 320
4. Calculate the new population mean:
µ (new) = sum_new / N
µ (new) = 320 / 20
µ (new) = 16
Therefore, the value for the new population mean is 16.