Counselor Education Comprehensive Exam (CECE) Practice Exam

Which of the following statements about skewed distributions is NOT TRUE?

1. Can be positively skewed

2. Can be negatively skewed

3. Scores accumulate at the center

4. Scores accumulate at one end

The correct answer is: Scores accumulate at the center

In the context of statistics, a skewed distribution refers to one where the data is not symmetrically distributed around a central value. When a distribution is positively skewed, it means that the tail on the right side of the distribution (higher values) is longer or fatter than the left side (lower values). Conversely, a negatively skewed distribution has a longer or fatter tail on the left side. The statement that scores accumulate at the center is not accurate in relation to skewed distributions. In skewed distributions, the accumulation of scores is not at the center but rather at one end, depending on whether the skew is positive or negative. In a positively skewed distribution, most scores cluster towards the lower end with a few high outliers extending the tail to the right. In a negatively skewed distribution, the situation is inverted, where most scores cluster at the higher end with a few low outliers extending the tail to the left. Thus, it is true that scores accumulate at one end in skewed distributions, rather than clustering around the center. This reinforces the understanding that in a skewed distribution, the data does not follow the bell-curve shape typical of normal distributions where scores would be centered.