Strange distribution of the 2011 11+ results (statistically)

[TA123]

We are appealing against non-selection and have recently received our case papers, which include everything we sent for the appeal as well as a report on 11+ results in Bucks. Among all other information it have a graph showing the distribution of the results, basically how many students reached any particular score, from 69 up to 141. Overall the results seem to be normally distributed. I mean that the medium/average marks were received by the highest number of students, while the closer the marks to both extremes (69 and 141) the lower number of students received them. That makes sense as the results should be normally distributed. What I cannot understand is that the highest mark (141) has the highest number of students achieving it, which does not make any sense from the statistical point of view. It’s like the 139 mark was achieved by (I do not remember the exact number) 15, students, 140 – by 10 students and 141 by 320 students.

I am sorry if the post is a bit too technical, but what I want to say is that the results around the mean usually achieved by the highest number of people, while the results closer to both ends of the spectre are achieved by less and less people the closer they are to the extremes. So from the statistical point of view there should be should not be this huge difference between how many students got 140 and 141 and the number of the latter should be lower than the former.

Probably there is an explanation for that so I wonder if anyone knows it. Or if the situation was similar in previous years?

[wurzel]

This is simply because children can actually get a raw score that equates to significantly more than 141, but there is no point (for the purposes of the test) in discriminating between those scores at the top end of the distribution, so they lump them all together and give a maximum value of 141. The exact normalised score becomes very unreliable up at this end anyway. The same 'tail' effect is true at the lower end, but they don't seem to do the cut-off in the same way there.

[Sally-Anne]

Perfectly explained, wurzel. And yes, it is always the same.

In areas where score is used as a determining factor for admission children have been known to achieve scores as high as 149, and the "bell curve" tapers off at both ends.

[TA123]

Thanks a lot for the great explanation. I was suspecting something like this. I just thought if you had 100% questions correctly answered you got 141, but I guess it's not the case.