-A set of seven scores has a mean of 10. If one of the scores is changed from X=15 to X=1, what will be the new value for the new mean?
-A sample of n=8 scores has a mean of M=12. One new score is added to the same and the new mean is found to be M=13. What is the vaule of the new score?
What steps do I follow to figure out these types of problems? I don't quite understand how the book is explaining it.
If a set of seven numbers has a mean of 10, then the sum of the ten numbers must be 70. If you raise one of thme from 1 to 15, than the total becomes 84. Divide that by 7 for the new mean value.
Use a similar approach for the second question. The total for the first 8 numbers is 8x12 = 96. When a ninth number is added, the total becomes 9x13 = 117. How much did the thirteenth number add to the total?
To solve problems like these, you need to understand the concept of mean and how it is affected when a score is changed or added.
1. Calculation of the new mean when one score is changed:
a. Start by calculating the sum of the original set of scores. In this case, the sum of the original set of scores is 7 * 10 = 70.
b. Subtract the old score you want to change from the sum. So, 70 - 15 = 55.
c. Add the new score to the sum. Therefore, 55 + 1 = 56.
d. Divide the new sum by the total number of scores. Since one score has been changed, the total number of scores remains the same, which is 7. So, 56/7 = 8.
e. Therefore, the new mean is 8.
2. Calculation of the new score when the mean is changed:
a. Calculate the sum of the original set of scores by multiplying the mean by the total number of scores. In this case, 12 * 8 = 96.
b. Calculate the sum of the new set of scores by multiplying the new mean by the new total number of scores (original number plus the added score). So, 13 * (8 + 1) = 117.
c. Subtract the original sum from the new sum. Therefore, 117 - 96 = 21.
d. Therefore, the new score is 21.
Remember to understand the basic concepts of mean, how to calculate sum, and how these calculations change when scores are added or changed. By following these steps, you can accurately solve similar problems.