On average, young people from poor families had test scores between three and four points below which is expected for their age group. 

between three and four points below which is expected for their age group这是一个介词短语作定语修饰test scores. 介词below被between three and four points前置修饰，below后接名词性从句。which引导名词性从句时只能是疑问词，而这个名词从句并没有疑问意义，所以用which为错误。what为融合型关系代词引导名词性关系分句，what=that which.