Question
A psychologist investigated differences in conformity between two age groups. Each participant completed a questionnaire to assess their level of conformity and was given an overall score. The higher the score, the higher the level of conformity. The psychologist then calculated average scores for each age group.
The results of the study are given in the table below.
Average conformity scores for the two age groups
Measures of central tendency | Group A Ages 11–15 | Group B Ages 16–20 |
Mean | 25 | 25 |
Median | 29 | 21 |
Mode | 33 | 18 |
(a) Identify the type of distribution that the data suggest for each of Groups A and B.
In each case justify your answer. [4 marks]
(b) Explain what the difference in mode values of the two age groups shows. [2 marks]
Answer
(a) Group A has a negatively skewed distribution. This is because the mean (25) is lower than the median (29) and mode (33). Group B has a positively skewed distribution. This is because the mean (25) is higher than the median (21) and mode (18).
(b) The mode values show us that the most frequent conformity score (33) in the younger age group (Group A) was a lot higher than the most frequent conformity score (18) in the older age group (Group B).
Examiner Comment: To gain full marks, students needed to demonstrate an understanding of the negatively and positively skewed distributions and accurately apply this to the data by comparing the mean, median, and mode for each group. They also needed to understand that the mode represents the most common score and use this to justify their conclusions.