Question

the following are the scores of 25 students who participated in a psychology experiment. The scores represent the number of trials required to complete a memorization test.

12, 10, 12, 11, 6, 15, 14, 17, 9, 12, 13, 8, 7, 15, 14, 15, 18, 19, 14, 10, 14, 14, 16, 8, 9

Based on these data, the z score for generated for a person with a raw score of 6 is___ and their percentile is___

Answer 1

Answer :

Z-score = (x-mean)/ standard deviation

for the given data -

mean = (12+10+12+11+ 6+15+14+17+9+12+13+8+7+15+14+15+18+19+ 14+10+14+14+16+8+9)/25 = 1248

variance . = sum of square (x(i)-mean) / n-1

= 12.01

s.d. = 3.46

therefor z-score for the raw data 6 is -

Z-score = 6-12.48/3.46 = -1.872

To calculate the k^th percentile (where k is any number between zero and one hundred), do the following steps:

1. Order all the values in the data set from smallest to largest.

2. Multiply k percent by the total number of values, n

3. If the index obtained in Step 2 is not a whole number, round it up to the nearest whole number and go to Step 4a. If the index obtained in Step 2 is a whole number, go to Step 4b.

4. 4a.Count the values in your data set from left to right (from the smallest to the largest value) until you reach the number indicated by Step 3.

The corresponding value in your data set is the k^th percentile.

5. 4b.Count the values in your data set from left to right until you reach the number indicated by Step 2.

The k^th percentile is the average of that corresponding value in your data set and the value that directly follows it.