A population of scores has a mean of µ = 26, a median of 23, and a mode of 22. What is the most likely shape for the population distribution?
Question
A population of scores has a mean of µ = 26, a median of 23, and a mode of 22. What is the most likely shape for the population distribution?
Solution
To determine the most likely shape for the population distribution given the mean, median, and mode, we can analyze the relationship between these three measures of central tendency.
- Mean (µ) = 26
- Median = 23
- Mode = 22
When the mean is greater than the median, and the median is greater than the mode, the distribution is typically positively skewed (or right-skewed). This means that the tail on the right side of the distribution is longer or fatter than the left side.
Therefore, the most likely shape for the population distribution is positively skewed.
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