Please help ASAP

Hello everyone,

can you please help me on a few problems:

1)The mean of a set of test scores is 83. If a score of 85 is added to the set and a new mean is calcuated:
Choose One: a)the new mean is greater than 83, b)the new mean is less than 83, c)the new mean is 83, d)the effect cannot be determined
I picked choice D, am I correct?

2)It lists a table:
Size Frequency
5 2
6 4
7 5
8 6
9 3

The question is find the mean of these shoe sizes:
choose one: a)7.0 b)7.2 c)7.8 d)8.4

3)Again, it lists a table:
Stem Leaf
3 3 5
4 4 4 6 8
5 0 1 3 7 9 9
6 2 2 5 8
Key:3/3=33
The question is find the median of this stem and leaf plot.
choose one: a)50 b)52 c)52.25 d)59, Im not sure how to solve, but I am thinking it is d, 59. Please tell me if I am correct.

4)The average of A and B is 6. The average of X,Y, and Z is 16. What is the average of A,B,X,Y,and Z? Please help me I have no idea how to do this problem.

5)The average grade on a test taken by 20 students was 75. When one more student took the test after school, the class average became a 76. What score did that student recieve? I believe it is a 100 he recieved on the test. Please help me on that.

6)The average of four different positive integers is 9. What is the greatest value for one of the integers? Please help me I have no idea how to do this.

Thanks in advance,
Ryan

Hello, Ryan!

Are you <u>sure</u> you know what an average is?

4) The average of A and B is 6.
The average of X,Y, and Z is 16.
What is the average of A,B,X,Y,and Z?

Click to expand...

How can we find the average of A, B, X, Y, Z?
We must find their <u>sum</u> . . . and divide by 5.

Do we know their sum? . . . no.
Can we find their sum? . . . yes!

"The average of A and B is 6."
This means: .\(\displaystyle \frac{A\,+\,B}{2}\,=\,6\;\;\Rightarrow\;\;A\,+\,B\:=\:12\)

"The average of X,Y,Z is 16."
This means: .\(\displaystyle \frac{X\,+\,Y\,+\,Z}{3}\,=\,16\;\;\Rightarrow\;\;X\,+\,Y\,+\,Z\,=\,48\)

Hence: .\(\displaystyle (A\,+\,B)\,+\,(X\,+\,Y\,+\,Z)\;=\;12\,+\,48\;=\;60\)

Therefore, their average is: .\(\displaystyle \frac{60}{5}\,=\,12\)

5) The average grade on a test taken by 20 students was 75.
When one more student took the test after school, the class average became a 76.
What score did that student recieve?

Click to expand...

If the average of the 20 students was 75, their total score must have been: \(\displaystyle 20\,\times\,75\,=\,1500\)

The next student had a score of \(\displaystyle x\), so the class had a total of \(\displaystyle x\.+\,1500\) points.

The new average is: .\(\displaystyle \frac{x\,+\,1500}{21}\;=\;76\)

Solve for \(\displaystyle x.\)

6)The average of four different positive integers is 9.
What is the greatest value for one of the integers?

Click to expand...

This is a "thinking" problem . . .

Let the four positive integers be: \(\displaystyle a,\,b,\,c,\,d.\)

Since their average is 9: . \(\displaystyle \frac{a\,+\,b\,+\,c\,+\,d}{4}\:=\:9\;\;\Rightarrow\;\;a\,+\,b\,+\,c\,+\,d\:=\:36\)

To make \(\displaystyle a\) as large as possible, we make \(\displaystyle b,\,c,\,d\) as small as possible.

. . Since \(\displaystyle b,\,c,\,d\) are positive integers, their least value is \(\displaystyle 1.\)

And we have:. \(\displaystyle a\,+\,1\,+\,1\,+\,1\:=\:36\;\;\Rightarrow\;\;a\,=\,33\)