A classroom of n = 10 children has a mean score of 17.200 on a measure of hyperactivity. One new child is added to the class, and the mean hyperactivity score for the resulting classroom including all the children is 18.000. Find the value of the new child's hyperactivity score.
I don't really know how to even start this problem. Please help!
Think about how you obtained that mean?
didn't you add the total of the 10 children and divide by 10 ?
so the total must have been 172
Let the new kid's score be x
then (172+x)/11 = 18
172+x = 198
x = 26
How did you get 198?
To solve this problem, we can use the concept of the mean (average) score and apply it to the given information.
Let's break down the information provided:
1. A classroom of "n=10" children has a mean score of "17.200" on the hyperactivity measure.
2. One new child is added to the class.
3. The mean hyperactivity score for the resulting classroom, including all the children, is "18.000".
To find the value of the new child's hyperactivity score, we need to consider the effect of the new child on the average score of the classroom.
Here's how we can approach the problem:
Step 1: Calculate the sum of the hyperactivity scores for the original 10 children.
To find the sum, we can multiply the mean score by the number of children:
Sum = Mean × Number of Children
Sum = 17.200 × 10
Sum = 172.000
Step 2: Calculate the sum of the hyperactivity scores for all the children in the resulting classroom.
Since the mean score for the resulting classroom is given as 18.000, we can find the sum by multiplying the new mean by the total number of children (n + 1):
Sum = Mean × (Number of Children + 1)
Sum = 18.000 × (10 + 1)
Sum = 198.000
Step 3: Find the hyperactivity score of the new child.
To find the score of the new child, we can subtract the sum of the original 10 children from the sum including the new child:
New Child's Score = Sum including New Child - Sum of Original 10 Children
New Child's Score = 198.000 - 172.000
New Child's Score = 26.000
Therefore, the hyperactivity score of the new child is 26.000.