A population of N=8 scores has a mean of µ = 20. If one score is changed from X=14 to X=50, what will be the value for the new mean?
Mean = Σ(scores)/N
20 = x/8
160 = Σ(scores)
With 36 additional points, Σ(scores) = 196
New Mean = 196/8
To find the new mean, we need to calculate the sum of all the scores and divide it by the total number of scores. Here's how you can solve it step by step:
Step 1: Calculate the sum of the original scores.
The original scores have a mean of 20, so the sum of all the scores can be calculated using the formula:
Sum = Mean * Total Number of Scores
Sum = 20 * 8
Sum = 160
Step 2: Subtract the original score of 14 from the sum.
Since one score is changed from 14 to 50, we need to subtract 14 from the sum calculated in Step 1.
After subtracting 14, we get:
New Sum = Sum - 14
New Sum = 160 - 14
New Sum = 146
Step 3: Add the new score of 50 to the new sum.
Now we need to add the new score of 50 to the new sum calculated in Step 2.
After adding 50, we get:
New Sum = New Sum + 50
New Sum = 146 + 50
New Sum = 196
Step 4: Calculate the new mean.
To calculate the new mean, divide the new sum by the total number of scores, which is still 8 since only one score was changed.
New Mean = New Sum / Total Number of Scores
New Mean = 196 / 8
New Mean = 24.5
Therefore, the new mean is 24.5.