Statistics Help

Question

2. A sample of n=15 scores has a mean of M=6. One person with a score of X=22 is added to the sample. What is the value for the new sample mean?

3. A population of N=15 scores has a mean of µ=8. One score in the population is changed from X=20 to X=5. What is the value for the new population mean?

4. A sample of n=7 scores has a mean of M=5. After one new score is added to the sample, the new mean is found to be M=6. What is the value for the new score?

5. One sample of n=12 scores has a mean of M=7 and a second sample of n=8 scores has a mean of M=12. If the two samples are combined, what is the mean for the combined sample?

Answer 1

Hi Cassie,

 

2.  If the mean of 15 scores is 6, then we need to first find the sum of those 15 scores.

6*15 = 90

Now we can add 22 to this

90+22=112

and divide by the new n which is 16

112/16 = 7 <-- the new mean

 

3. This problem can be solved the same way

If µ=8 and N=15, then the sum of the scores was 8*15 = 120

Now, one of the scores was changed.  It was originally included at 20 but it is corrected to 5.

120 - 20 + 5 = 105

Now in this problem N does not change.

105/15 = 7 <-- the new mean

 

4. M=5 and n=7

Mn = 35

Now add one more score so that M=6 and n=8

New Mn = 6*8=48

The difference between these two Mn's is the value of the new score

48-35=13

 

5. Sample 1:  n=12 M=7  Mn = 84

Sample 2: n=8 M=12       Mn = 96

To get the combined mean, add together the two Mn's and divide by the sum of the n's.

(84+96)/(12+8) = 180/20 = 9