Q1. (10 points) The following data are 12 scores from Quiz #1 in this course. a)

Question

Q1. (10 points) The following data are 12 scores from Quiz #1 in this course. a) (2 points) Rearrange the data in order from smallest to largest. Then assign each observation a rank. Ra 3028.5 3030 30 302822.5 27 29.529 17 17 22.5 2728 28.5 29 29.5 3030 30 30 30 Rank b) (2 points) Which rank is associated with the score 28? c) (2 points) Which rank is associated with the score 30? d) (2 points) What score is associated with rank 7? e) (2 points) Check it! It is known from mathematics that the sum of whole numbers from 1 up to any number is equal to Take the sum of your ranks. Do they sum to the same amount as 1-11? call this "n”, (Ex. 1+2+3+4+ +(n-1)+n), This means that the sum of ranks 1 to 11 should 11x12

Explanation / Answer

a) Rank Observations

1. 17

2. 22.5

3. 27

4. 28

5. 28.5

6. 29

7. 29.5

8. 30

8. 30

8. 30

8. 30

8. 30

b) Rank of score 28 is = 4.

c) Rank of score 30 is = 8.

d) Score with rank 7 is = 29.5.

e) Here the sum will not be equal to the sum of 12 consecutive

numbers (1 to 12) as, we have ties. For instance, 30 is

repeated 5 times in the dataset. So the rank associated with

all the observations with value 30 is same, which is 8 in this

case.

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