Statistic Help.

Question

3. A sample of n = 9 scores has a M = 8. If on of the scores with a value of X = 12 is

removed from the sample of scores, what is the new mean for the remaining sample?

4. A sample of scores has a M = 12. If each score in the sample is multiplied by 4, what will the mean of the sample become?

5. A sample of n = 13 has a M = 6. If one more score is added to the sample and the mean changes to M = 6.5, what is the value of the new score?

6. What is a deviation from the mean score? Write out what it looks like in mathematical

terms.

7. A sample has a M = 10. If five points are added to each score, what will the new mean of the sample be?

Answer 1

3) As you know, to get the mean (μ) of a set of samples, you add up the samples and divide by the number of samples:

In this case, we can replace one of the samples with 12 (let's say it is s₃) and we can input μ = 8 and n = 9:

8 = (s₁ + s₂ + 12 + s₄ + . . . s₉)/9 and multiplying both sides by 9 we get:

72 = s₁ + s₂ + 12 + s₄ + . . . s₉ then subtraction 12 from both sides we get:

60 = s₁ + s₂ + s₄ + . . . s₉

To find the new mean, we take the sum of the samples (which is s₁ + s₂ + s₄ + . . . s_n or 60) and divide by the new number of samples n = 8

μ_new = 60/8 = 7.5

4) If 12 = μ = (s₁ + s₂ + . . . s_n)/n then 4•12 = 4(s₁ + s₂ + . . . s_n)/n or 4•12 = (4s₁ + 4s₂ + . . . 4s_n)/n meaning the new mean would be 4•12 or 48.

The other problems are similar to problem 3. Give them a try.