Given:
Mode =31.5
Mean =34.5
For a moderately asymmetrical distribution, the relationship between mean, median, and mode is:
Mean − Mode =3(Mean − Median)
This is Karl Pearson's empirical relationship for moderately skewed distributions.
Substituting the given values:
34.5−31.5=3(34.5−Median)
3=3(34.5−Median)
Dividing by 3:
1=34.5−Median
Median=34.5−1
Median=33.5