In a normal distribution of scores, four participants obtained the following deviation
scores: 11, 22, 15, and 210. (a) Which score reflects the highest raw score? (b) Which score reflects the lowest raw score? (c) Rank-order the deviation scores in terms of their frequency, starting with the score with the lowest frequency.
Assume that the data in question 25 reflect a highly skewed interval variable.
(a) What statistics would you compute to summarize these conditions? (b) We compute them to be 14, 12, and 8.5, respectively. What conclusion about the study should you draw? (c) What conclusion would you draw about the populations produced by this experiment?
To answer these questions, we need to understand deviation scores and how they relate to the raw scores in a normal distribution.
Deviation scores are calculated by subtracting the mean from each raw score. In a normal distribution, the mean is zero, so the deviation score represents how much a particular score deviates from the mean.
(a) To find the highest raw score, we need to look for the deviation score that has the highest value. Among the given deviation scores: 11, 22, 15, and 210, the score with the highest deviation score is 210. This indicates that the corresponding raw score is the highest.
(b) Similarly, to find the lowest raw score, we need to look for the deviation score with the lowest value. Among the provided deviation scores, the score with the lowest deviation score is 11. Therefore, the corresponding raw score is the lowest.
(c) To rank-order the deviation scores in terms of their frequency, we need additional information about the number of participants who obtained each score. If we assume that these are the only participants and each score represents one participant, the frequency would be as follows:
Frequency: 1, 1, 1, 1
In this case, all the deviation scores have the same frequency, so we cannot rank-order them based on frequency. However, if we had more information about the number of participants for each score, we could determine the frequency and rank-order accordingly.